generateTriangulations -- generate all triangulations with certain properties

Synopsis

Usage:

Ts = generateTriangulations A

Ts = generateTriangulations(A, tri)

Ts = generateTriangulations T
Inputs:
- A, a matrix, over the integers (or rationals?), whose columns are the points to use
- tri, a list, A list of lists of indices representing a triangulation of the columns of $A$
- T, an instance of the type Triangulation (missing documentation) , packages both $A$ and tri in one object
Optional inputs:
- Limit => an integer, default value infinity, Stop after constructing this many triangulations
- RegularOnly => a Boolean value, default value false, Only generate regular triangulations
- Homogenize => a Boolean value, default value true, set to false in the case the columns form a vector configuration. The default case is that the columns of $A$ are considered a point configuration (not used in the variant generateTriangulations T)
Outputs:
- Ts, a list, of lists of integers, each such list represents a triangulation

Description

This function can be used to generate a set of triangulations of a point set or vector configuration $A$ (the points are the columns of $A$).

It operates by starting with one triangulation (tri or T), if one is given, and if not, it constructs a fine triangulation of the set of columns of $A$.

After this, it uses bistellar flips to generate neighbors, and continues, until the limit is reached, or no new ones can be constructed.

Important note! This function generally starts with a fine triangulation (i.e. one using all of the points in $A$), and only considers bistellar flips that give fine triangulations.

i1 : A = vertices hypercube 3

o1 = | -1 1  -1 1  -1 1  -1 1 |
     | -1 -1 1  1  -1 -1 1  1 |
     | -1 -1 -1 -1 1  1  1  1 |

              3       8
o1 : Matrix QQ  <-- QQ

i2 : T = topcomRegularFineTriangulation A

o2 = {{0, 1, 2, 4}, {1, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 6}, {3, 4, 5, 6},
     ------------------------------------------------------------------------
     {3, 5, 6, 7}}

o2 : List

i3 : tri = regularFineTriangulation A

o3 = triangulation {{0, 1, 2, 4}, {1, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 6}, {3, 4, 5, 6}, {3, 5, 6, 7}}

o3 : Triangulation

i4 : Ts1 = generateTriangulations A -- list of Triangulation's.

o4 = {triangulation {{0, 1, 3, 7}, {0, 1, 5, 7}, {0, 2, 3, 7}, {0, 2, 6, 7},
     ------------------------------------------------------------------------
     {0, 4, 5, 7}, {0, 4, 6, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 5, 7},
     ------------------------------------------------------------------------
     {0, 2, 3, 7}, {0, 2, 4, 7}, {0, 4, 5, 7}, {2, 4, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 3, 5}, {0, 2, 3, 7}, {0, 2, 6, 7}, {0, 3, 5, 7}, {0, 4, 5, 6},
     ------------------------------------------------------------------------
     {0, 5, 6, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 4, 7}, {0, 2, 3, 6},
     ------------------------------------------------------------------------
     {0, 3, 6, 7}, {0, 4, 6, 7}, {1, 4, 5, 7}}, triangulation {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 5, 7}, {0, 3, 6, 7}, {0, 4, 5, 6}, {0, 5, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 2, 5}, {0, 2, 5, 6}, {0, 4, 5, 6}, {1, 2, 3, 5},
     ------------------------------------------------------------------------
     {2, 3, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 3, 4}, {0, 2, 3, 4},
     ------------------------------------------------------------------------
     {1, 3, 4, 5}, {2, 3, 4, 7}, {2, 4, 6, 7}, {3, 4, 5, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 3, 5}, {0, 2, 3, 4}, {0, 3, 4, 5}, {2, 3, 4, 6}, {3, 4, 5, 7},
     ------------------------------------------------------------------------
     {3, 4, 6, 7}}, triangulation {{0, 1, 3, 4}, {0, 2, 3, 6}, {0, 3, 4, 6},
     ------------------------------------------------------------------------
     {1, 3, 4, 5}, {3, 4, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 2, 5},
     ------------------------------------------------------------------------
     {0, 2, 4, 5}, {1, 2, 3, 5}, {2, 3, 5, 6}, {2, 4, 5, 6}, {3, 5, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 2, 4}, {1, 2, 3, 5}, {1, 2, 4, 5}, {2, 3, 5, 7},
     ------------------------------------------------------------------------
     {2, 4, 5, 6}, {2, 5, 6, 7}}, triangulation {{0, 1, 2, 6}, {0, 1, 4, 6},
     ------------------------------------------------------------------------
     {1, 2, 3, 6}, {1, 3, 6, 7}, {1, 4, 5, 6}, {1, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 4}, {1, 2, 3, 4}, {1, 3, 4, 7}, {1, 4, 5, 7}, {2, 3, 4, 7},
     ------------------------------------------------------------------------
     {2, 4, 6, 7}}, triangulation {{0, 1, 3, 6}, {0, 1, 4, 6}, {0, 2, 3, 6},
     ------------------------------------------------------------------------
     {1, 3, 6, 7}, {1, 4, 5, 6}, {1, 5, 6, 7}}, triangulation {{0, 1, 2, 5},
     ------------------------------------------------------------------------
     {0, 2, 4, 5}, {1, 2, 3, 7}, {1, 2, 5, 7}, {2, 4, 5, 6}, {2, 5, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 2, 7}, {0, 1, 5, 7}, {0, 2, 4, 7}, {0, 4, 5, 7},
     ------------------------------------------------------------------------
     {1, 2, 3, 7}, {2, 4, 6, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 4, 7},
     ------------------------------------------------------------------------
     {0, 2, 3, 7}, {0, 2, 6, 7}, {0, 4, 6, 7}, {1, 4, 5, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 3, 5}, {0, 2, 3, 7}, {0, 2, 6, 7}, {0, 3, 5, 7}, {0, 4, 5, 7},
     ------------------------------------------------------------------------
     {0, 4, 6, 7}}, triangulation {{0, 1, 2, 7}, {0, 1, 4, 7}, {0, 2, 4, 7},
     ------------------------------------------------------------------------
     {1, 2, 3, 7}, {1, 4, 5, 7}, {2, 4, 6, 7}}, triangulation {{0, 1, 2, 5},
     ------------------------------------------------------------------------
     {0, 2, 4, 5}, {1, 2, 3, 7}, {1, 2, 5, 7}, {2, 4, 5, 7}, {2, 4, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 2, 5}, {0, 2, 5, 6}, {0, 4, 5, 6}, {1, 2, 3, 7},
     ------------------------------------------------------------------------
     {1, 2, 5, 7}, {2, 5, 6, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 4, 7},
     ------------------------------------------------------------------------
     {0, 2, 3, 7}, {0, 2, 4, 7}, {1, 4, 5, 7}, {2, 4, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 3, 6}, {0, 1, 4, 6}, {0, 2, 3, 6}, {1, 3, 6, 7}, {1, 4, 5, 7},
     ------------------------------------------------------------------------
     {1, 4, 6, 7}}, triangulation {{0, 1, 3, 6}, {0, 1, 5, 6}, {0, 2, 3, 6},
     ------------------------------------------------------------------------
     {0, 4, 5, 6}, {1, 3, 6, 7}, {1, 5, 6, 7}}, triangulation {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 5, 7}, {0, 3, 6, 7}, {0, 4, 5, 7}, {0, 4, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 3, 5}, {0, 2, 3, 5}, {0, 2, 5, 6}, {0, 4, 5, 6},
     ------------------------------------------------------------------------
     {2, 3, 5, 7}, {2, 5, 6, 7}}, triangulation {{0, 1, 2, 4}, {1, 2, 3, 7},
     ------------------------------------------------------------------------
     {1, 2, 4, 5}, {1, 2, 5, 7}, {2, 4, 5, 6}, {2, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 5}, {0, 2, 4, 5}, {1, 2, 3, 5}, {2, 3, 5, 7}, {2, 4, 5, 6},
     ------------------------------------------------------------------------
     {2, 5, 6, 7}}, triangulation {{0, 1, 3, 4}, {0, 2, 3, 6}, {0, 3, 4, 6},
     ------------------------------------------------------------------------
     {1, 3, 4, 5}, {3, 4, 5, 7}, {3, 4, 6, 7}}, triangulation {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 4, 5}, {0, 3, 4, 6}, {3, 4, 5, 6}, {3, 5, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 3, 5}, {0, 2, 3, 5}, {0, 2, 4, 5}, {2, 3, 5, 6},
     ------------------------------------------------------------------------
     {2, 4, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 2, 4}, {1, 2, 3, 6},
     ------------------------------------------------------------------------
     {1, 2, 4, 6}, {1, 3, 5, 6}, {1, 4, 5, 6}, {3, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 4}, {1, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 6}, {3, 4, 5, 6},
     ------------------------------------------------------------------------
     {3, 5, 6, 7}}, triangulation {{0, 1, 2, 4}, {1, 2, 3, 5}, {1, 2, 4, 5},
     ------------------------------------------------------------------------
     {2, 3, 5, 7}, {2, 4, 5, 7}, {2, 4, 6, 7}}, triangulation {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 4}, {0, 3, 4, 5}, {2, 3, 4, 7}, {2, 4, 6, 7}, {3, 4, 5, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 3, 4}, {0, 2, 3, 6}, {0, 3, 4, 6}, {1, 3, 4, 7},
     ------------------------------------------------------------------------
     {1, 4, 5, 7}, {3, 4, 6, 7}}, triangulation {{0, 1, 3, 4}, {0, 2, 3, 4},
     ------------------------------------------------------------------------
     {1, 3, 4, 7}, {1, 4, 5, 7}, {2, 3, 4, 7}, {2, 4, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 6}, {0, 1, 4, 6}, {1, 2, 3, 7}, {1, 2, 6, 7}, {1, 4, 5, 6},
     ------------------------------------------------------------------------
     {1, 5, 6, 7}}, triangulation {{0, 1, 2, 6}, {0, 1, 4, 6}, {1, 2, 3, 6},
     ------------------------------------------------------------------------
     {1, 3, 6, 7}, {1, 4, 5, 7}, {1, 4, 6, 7}}, triangulation {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 5, 6}, {0, 4, 5, 6}, {3, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 4}, {1, 2, 3, 7}, {1, 2, 4, 7}, {1, 4, 5, 7}, {2, 4, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 2, 7}, {0, 1, 5, 7}, {0, 2, 6, 7}, {0, 4, 5, 6},
     ------------------------------------------------------------------------
     {0, 5, 6, 7}, {1, 2, 3, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 5, 7},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 6, 7}, {0, 4, 5, 6}, {0, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 6}, {0, 1, 4, 6}, {1, 2, 3, 7}, {1, 2, 6, 7}, {1, 4, 5, 7},
     ------------------------------------------------------------------------
     {1, 4, 6, 7}}, triangulation {{0, 1, 2, 4}, {1, 2, 3, 4}, {1, 3, 4, 7},
     ------------------------------------------------------------------------
     {1, 4, 5, 7}, {2, 3, 4, 6}, {3, 4, 6, 7}}, triangulation {{0, 1, 2, 4},
     ------------------------------------------------------------------------
     {1, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 6}, {3, 4, 5, 7}, {3, 4, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 3, 4}, {0, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 6},
     ------------------------------------------------------------------------
     {3, 4, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 2, 4}, {1, 2, 3, 6},
     ------------------------------------------------------------------------
     {1, 2, 4, 6}, {1, 3, 6, 7}, {1, 4, 5, 6}, {1, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 4}, {1, 2, 3, 7}, {1, 2, 4, 6}, {1, 2, 6, 7}, {1, 4, 5, 6},
     ------------------------------------------------------------------------
     {1, 5, 6, 7}}, triangulation {{0, 1, 3, 5}, {0, 2, 3, 5}, {0, 2, 4, 5},
     ------------------------------------------------------------------------
     {2, 3, 5, 7}, {2, 4, 5, 6}, {2, 5, 6, 7}}, triangulation {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 4, 5}, {0, 3, 4, 6}, {3, 4, 5, 7}, {3, 4, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 3, 6}, {0, 1, 5, 6}, {0, 2, 3, 6}, {0, 4, 5, 6},
     ------------------------------------------------------------------------
     {1, 3, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 2, 5}, {0, 2, 5, 6},
     ------------------------------------------------------------------------
     {0, 4, 5, 6}, {1, 2, 3, 5}, {2, 3, 5, 7}, {2, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 5}, {0, 2, 4, 5}, {1, 2, 3, 5}, {2, 3, 5, 7}, {2, 4, 5, 7},
     ------------------------------------------------------------------------
     {2, 4, 6, 7}}, triangulation {{0, 1, 2, 4}, {1, 2, 3, 7}, {1, 2, 4, 5},
     ------------------------------------------------------------------------
     {1, 2, 5, 7}, {2, 4, 5, 7}, {2, 4, 6, 7}}, triangulation {{0, 1, 2, 6},
     ------------------------------------------------------------------------
     {0, 1, 5, 6}, {0, 4, 5, 6}, {1, 2, 3, 6}, {1, 3, 6, 7}, {1, 5, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 2, 7}, {0, 1, 5, 7}, {0, 2, 6, 7}, {0, 4, 5, 7},
     ------------------------------------------------------------------------
     {0, 4, 6, 7}, {1, 2, 3, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 5, 7},
     ------------------------------------------------------------------------
     {0, 2, 3, 7}, {0, 2, 6, 7}, {0, 4, 5, 6}, {0, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 7}, {0, 1, 4, 7}, {0, 2, 6, 7}, {0, 4, 6, 7}, {1, 2, 3, 7},
     ------------------------------------------------------------------------
     {1, 4, 5, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 5, 7}, {0, 2, 3, 6},
     ------------------------------------------------------------------------
     {0, 3, 6, 7}, {0, 4, 5, 7}, {0, 4, 6, 7}}, triangulation {{0, 1, 2, 6},
     ------------------------------------------------------------------------
     {0, 1, 5, 6}, {0, 4, 5, 6}, {1, 2, 3, 7}, {1, 2, 6, 7}, {1, 5, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 3, 5}, {0, 2, 3, 7}, {0, 2, 4, 7}, {0, 3, 5, 7},
     ------------------------------------------------------------------------
     {0, 4, 5, 7}, {2, 4, 6, 7}}, triangulation {{0, 1, 3, 5}, {0, 2, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 4, 5}, {2, 3, 5, 7}, {2, 4, 5, 7}, {2, 4, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 3, 4}, {0, 2, 3, 4}, {1, 3, 4, 7}, {1, 4, 5, 7}, {2, 3, 4, 6},
     ------------------------------------------------------------------------
     {3, 4, 6, 7}}, triangulation {{0, 1, 3, 6}, {0, 1, 4, 6}, {0, 2, 3, 6},
     ------------------------------------------------------------------------
     {1, 3, 5, 6}, {1, 4, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 2, 4},
     ------------------------------------------------------------------------
     {1, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 7}, {2, 4, 6, 7}, {3, 4, 5, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 3, 5}, {0, 2, 3, 4}, {0, 3, 4, 5}, {2, 3, 4, 6},
     ------------------------------------------------------------------------
     {3, 4, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 2, 4}, {1, 2, 3, 5},
     ------------------------------------------------------------------------
     {1, 2, 4, 5}, {2, 3, 5, 6}, {2, 4, 5, 6}, {3, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 3, 4}, {0, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 6}, {3, 4, 5, 7},
     ------------------------------------------------------------------------
     {3, 4, 6, 7}}, triangulation {{0, 1, 2, 6}, {0, 1, 4, 6}, {1, 2, 3, 6},
     ------------------------------------------------------------------------
     {1, 3, 5, 6}, {1, 4, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 2, 6},
     ------------------------------------------------------------------------
     {0, 1, 5, 6}, {0, 4, 5, 6}, {1, 2, 3, 6}, {1, 3, 5, 6}, {3, 5, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 2, 4}, {1, 2, 3, 6}, {1, 2, 4, 6}, {1, 3, 6, 7},
     ------------------------------------------------------------------------
     {1, 4, 5, 7}, {1, 4, 6, 7}}, triangulation {{0, 1, 3, 5}, {0, 2, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 5, 6}, {0, 4, 5, 6}, {2, 3, 5, 6}, {3, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 4}, {1, 2, 3, 7}, {1, 2, 4, 6}, {1, 2, 6, 7}, {1, 4, 5, 7},
     ------------------------------------------------------------------------
     {1, 4, 6, 7}}}

o4 : List

i5 : Ts2 = generateTriangulations(A, T) -- list of list of subsets

o5 = {{{0, 1, 3, 7}, {0, 1, 5, 7}, {0, 2, 3, 7}, {0, 2, 6, 7}, {0, 4, 5, 7},
     ------------------------------------------------------------------------
     {0, 4, 6, 7}}, {{0, 1, 3, 7}, {0, 1, 5, 7}, {0, 2, 3, 7}, {0, 2, 4, 7},
     ------------------------------------------------------------------------
     {0, 4, 5, 7}, {2, 4, 6, 7}}, {{0, 1, 3, 5}, {0, 2, 3, 7}, {0, 2, 6, 7},
     ------------------------------------------------------------------------
     {0, 3, 5, 7}, {0, 4, 5, 6}, {0, 5, 6, 7}}, {{0, 1, 3, 7}, {0, 1, 4, 7},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 6, 7}, {0, 4, 6, 7}, {1, 4, 5, 7}}, {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 5, 7}, {0, 3, 6, 7}, {0, 4, 5, 6}, {0, 5, 6, 7}},
     ------------------------------------------------------------------------
     {{0, 1, 2, 5}, {0, 2, 5, 6}, {0, 4, 5, 6}, {1, 2, 3, 5}, {2, 3, 5, 6},
     ------------------------------------------------------------------------
     {3, 5, 6, 7}}, {{0, 1, 3, 4}, {0, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 7},
     ------------------------------------------------------------------------
     {2, 4, 6, 7}, {3, 4, 5, 7}}, {{0, 1, 3, 5}, {0, 2, 3, 4}, {0, 3, 4, 5},
     ------------------------------------------------------------------------
     {2, 3, 4, 6}, {3, 4, 5, 7}, {3, 4, 6, 7}}, {{0, 1, 3, 4}, {0, 2, 3, 6},
     ------------------------------------------------------------------------
     {0, 3, 4, 6}, {1, 3, 4, 5}, {3, 4, 5, 6}, {3, 5, 6, 7}}, {{0, 1, 2, 5},
     ------------------------------------------------------------------------
     {0, 2, 4, 5}, {1, 2, 3, 5}, {2, 3, 5, 6}, {2, 4, 5, 6}, {3, 5, 6, 7}},
     ------------------------------------------------------------------------
     {{0, 1, 2, 4}, {1, 2, 3, 5}, {1, 2, 4, 5}, {2, 3, 5, 7}, {2, 4, 5, 6},
     ------------------------------------------------------------------------
     {2, 5, 6, 7}}, {{0, 1, 2, 6}, {0, 1, 4, 6}, {1, 2, 3, 6}, {1, 3, 6, 7},
     ------------------------------------------------------------------------
     {1, 4, 5, 6}, {1, 5, 6, 7}}, {{0, 1, 2, 4}, {1, 2, 3, 4}, {1, 3, 4, 7},
     ------------------------------------------------------------------------
     {1, 4, 5, 7}, {2, 3, 4, 7}, {2, 4, 6, 7}}, {{0, 1, 3, 6}, {0, 1, 4, 6},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {1, 3, 6, 7}, {1, 4, 5, 6}, {1, 5, 6, 7}}, {{0, 1, 2, 5},
     ------------------------------------------------------------------------
     {0, 2, 4, 5}, {1, 2, 3, 7}, {1, 2, 5, 7}, {2, 4, 5, 6}, {2, 5, 6, 7}},
     ------------------------------------------------------------------------
     {{0, 1, 2, 7}, {0, 1, 5, 7}, {0, 2, 4, 7}, {0, 4, 5, 7}, {1, 2, 3, 7},
     ------------------------------------------------------------------------
     {2, 4, 6, 7}}, {{0, 1, 3, 7}, {0, 1, 4, 7}, {0, 2, 3, 7}, {0, 2, 6, 7},
     ------------------------------------------------------------------------
     {0, 4, 6, 7}, {1, 4, 5, 7}}, {{0, 1, 3, 5}, {0, 2, 3, 7}, {0, 2, 6, 7},
     ------------------------------------------------------------------------
     {0, 3, 5, 7}, {0, 4, 5, 7}, {0, 4, 6, 7}}, {{0, 1, 2, 7}, {0, 1, 4, 7},
     ------------------------------------------------------------------------
     {0, 2, 4, 7}, {1, 2, 3, 7}, {1, 4, 5, 7}, {2, 4, 6, 7}}, {{0, 1, 2, 5},
     ------------------------------------------------------------------------
     {0, 2, 4, 5}, {1, 2, 3, 7}, {1, 2, 5, 7}, {2, 4, 5, 7}, {2, 4, 6, 7}},
     ------------------------------------------------------------------------
     {{0, 1, 2, 5}, {0, 2, 5, 6}, {0, 4, 5, 6}, {1, 2, 3, 7}, {1, 2, 5, 7},
     ------------------------------------------------------------------------
     {2, 5, 6, 7}}, {{0, 1, 3, 7}, {0, 1, 4, 7}, {0, 2, 3, 7}, {0, 2, 4, 7},
     ------------------------------------------------------------------------
     {1, 4, 5, 7}, {2, 4, 6, 7}}, {{0, 1, 3, 6}, {0, 1, 4, 6}, {0, 2, 3, 6},
     ------------------------------------------------------------------------
     {1, 3, 6, 7}, {1, 4, 5, 7}, {1, 4, 6, 7}}, {{0, 1, 3, 6}, {0, 1, 5, 6},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 4, 5, 6}, {1, 3, 6, 7}, {1, 5, 6, 7}}, {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 5, 7}, {0, 3, 6, 7}, {0, 4, 5, 7}, {0, 4, 6, 7}},
     ------------------------------------------------------------------------
     {{0, 1, 3, 5}, {0, 2, 3, 5}, {0, 2, 5, 6}, {0, 4, 5, 6}, {2, 3, 5, 7},
     ------------------------------------------------------------------------
     {2, 5, 6, 7}}, {{0, 1, 2, 4}, {1, 2, 3, 7}, {1, 2, 4, 5}, {1, 2, 5, 7},
     ------------------------------------------------------------------------
     {2, 4, 5, 6}, {2, 5, 6, 7}}, {{0, 1, 2, 5}, {0, 2, 4, 5}, {1, 2, 3, 5},
     ------------------------------------------------------------------------
     {2, 3, 5, 7}, {2, 4, 5, 6}, {2, 5, 6, 7}}, {{0, 1, 3, 4}, {0, 2, 3, 6},
     ------------------------------------------------------------------------
     {0, 3, 4, 6}, {1, 3, 4, 5}, {3, 4, 5, 7}, {3, 4, 6, 7}}, {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 4, 5}, {0, 3, 4, 6}, {3, 4, 5, 6}, {3, 5, 6, 7}},
     ------------------------------------------------------------------------
     {{0, 1, 3, 5}, {0, 2, 3, 5}, {0, 2, 4, 5}, {2, 3, 5, 6}, {2, 4, 5, 6},
     ------------------------------------------------------------------------
     {3, 5, 6, 7}}, {{0, 1, 2, 4}, {1, 2, 3, 6}, {1, 2, 4, 6}, {1, 3, 5, 6},
     ------------------------------------------------------------------------
     {1, 4, 5, 6}, {3, 5, 6, 7}}, {{0, 1, 2, 4}, {1, 2, 3, 4}, {1, 3, 4, 5},
     ------------------------------------------------------------------------
     {2, 3, 4, 6}, {3, 4, 5, 6}, {3, 5, 6, 7}}, {{0, 1, 2, 4}, {1, 2, 3, 5},
     ------------------------------------------------------------------------
     {1, 2, 4, 5}, {2, 3, 5, 7}, {2, 4, 5, 7}, {2, 4, 6, 7}}, {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 4}, {0, 3, 4, 5}, {2, 3, 4, 7}, {2, 4, 6, 7}, {3, 4, 5, 7}},
     ------------------------------------------------------------------------
     {{0, 1, 3, 4}, {0, 2, 3, 6}, {0, 3, 4, 6}, {1, 3, 4, 7}, {1, 4, 5, 7},
     ------------------------------------------------------------------------
     {3, 4, 6, 7}}, {{0, 1, 3, 4}, {0, 2, 3, 4}, {1, 3, 4, 7}, {1, 4, 5, 7},
     ------------------------------------------------------------------------
     {2, 3, 4, 7}, {2, 4, 6, 7}}, {{0, 1, 2, 6}, {0, 1, 4, 6}, {1, 2, 3, 7},
     ------------------------------------------------------------------------
     {1, 2, 6, 7}, {1, 4, 5, 6}, {1, 5, 6, 7}}, {{0, 1, 2, 6}, {0, 1, 4, 6},
     ------------------------------------------------------------------------
     {1, 2, 3, 6}, {1, 3, 6, 7}, {1, 4, 5, 7}, {1, 4, 6, 7}}, {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 5, 6}, {0, 4, 5, 6}, {3, 5, 6, 7}}, {{0, 1, 2, 4},
     ------------------------------------------------------------------------
     {1, 2, 3, 7}, {1, 2, 4, 7}, {1, 4, 5, 7}, {2, 4, 6, 7}}, {{0, 1, 2, 7},
     ------------------------------------------------------------------------
     {0, 1, 5, 7}, {0, 2, 6, 7}, {0, 4, 5, 6}, {0, 5, 6, 7}, {1, 2, 3, 7}},
     ------------------------------------------------------------------------
     {{0, 1, 3, 7}, {0, 1, 5, 7}, {0, 2, 3, 6}, {0, 3, 6, 7}, {0, 4, 5, 6},
     ------------------------------------------------------------------------
     {0, 5, 6, 7}}, {{0, 1, 2, 6}, {0, 1, 4, 6}, {1, 2, 3, 7}, {1, 2, 6, 7},
     ------------------------------------------------------------------------
     {1, 4, 5, 7}, {1, 4, 6, 7}}, {{0, 1, 2, 4}, {1, 2, 3, 4}, {1, 3, 4, 7},
     ------------------------------------------------------------------------
     {1, 4, 5, 7}, {2, 3, 4, 6}, {3, 4, 6, 7}}, {{0, 1, 2, 4}, {1, 2, 3, 4},
     ------------------------------------------------------------------------
     {1, 3, 4, 5}, {2, 3, 4, 6}, {3, 4, 5, 7}, {3, 4, 6, 7}}, {{0, 1, 3, 4},
     ------------------------------------------------------------------------
     {0, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 6}, {3, 4, 5, 6}, {3, 5, 6, 7}},
     ------------------------------------------------------------------------
     {{0, 1, 2, 4}, {1, 2, 3, 6}, {1, 2, 4, 6}, {1, 3, 6, 7}, {1, 4, 5, 6},
     ------------------------------------------------------------------------
     {1, 5, 6, 7}}, {{0, 1, 2, 4}, {1, 2, 3, 7}, {1, 2, 4, 6}, {1, 2, 6, 7},
     ------------------------------------------------------------------------
     {1, 4, 5, 6}, {1, 5, 6, 7}}, {{0, 1, 3, 5}, {0, 2, 3, 5}, {0, 2, 4, 5},
     ------------------------------------------------------------------------
     {2, 3, 5, 7}, {2, 4, 5, 6}, {2, 5, 6, 7}}, {{0, 1, 3, 5}, {0, 2, 3, 6},
     ------------------------------------------------------------------------
     {0, 3, 4, 5}, {0, 3, 4, 6}, {3, 4, 5, 7}, {3, 4, 6, 7}}, {{0, 1, 3, 6},
     ------------------------------------------------------------------------
     {0, 1, 5, 6}, {0, 2, 3, 6}, {0, 4, 5, 6}, {1, 3, 5, 6}, {3, 5, 6, 7}},
     ------------------------------------------------------------------------
     {{0, 1, 2, 5}, {0, 2, 5, 6}, {0, 4, 5, 6}, {1, 2, 3, 5}, {2, 3, 5, 7},
     ------------------------------------------------------------------------
     {2, 5, 6, 7}}, {{0, 1, 2, 5}, {0, 2, 4, 5}, {1, 2, 3, 5}, {2, 3, 5, 7},
     ------------------------------------------------------------------------
     {2, 4, 5, 7}, {2, 4, 6, 7}}, {{0, 1, 2, 4}, {1, 2, 3, 7}, {1, 2, 4, 5},
     ------------------------------------------------------------------------
     {1, 2, 5, 7}, {2, 4, 5, 7}, {2, 4, 6, 7}}, {{0, 1, 2, 6}, {0, 1, 5, 6},
     ------------------------------------------------------------------------
     {0, 4, 5, 6}, {1, 2, 3, 6}, {1, 3, 6, 7}, {1, 5, 6, 7}}, {{0, 1, 2, 7},
     ------------------------------------------------------------------------
     {0, 1, 5, 7}, {0, 2, 6, 7}, {0, 4, 5, 7}, {0, 4, 6, 7}, {1, 2, 3, 7}},
     ------------------------------------------------------------------------
     {{0, 1, 3, 7}, {0, 1, 5, 7}, {0, 2, 3, 7}, {0, 2, 6, 7}, {0, 4, 5, 6},
     ------------------------------------------------------------------------
     {0, 5, 6, 7}}, {{0, 1, 2, 7}, {0, 1, 4, 7}, {0, 2, 6, 7}, {0, 4, 6, 7},
     ------------------------------------------------------------------------
     {1, 2, 3, 7}, {1, 4, 5, 7}}, {{0, 1, 3, 7}, {0, 1, 5, 7}, {0, 2, 3, 6},
     ------------------------------------------------------------------------
     {0, 3, 6, 7}, {0, 4, 5, 7}, {0, 4, 6, 7}}, {{0, 1, 2, 6}, {0, 1, 5, 6},
     ------------------------------------------------------------------------
     {0, 4, 5, 6}, {1, 2, 3, 7}, {1, 2, 6, 7}, {1, 5, 6, 7}}, {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 7}, {0, 2, 4, 7}, {0, 3, 5, 7}, {0, 4, 5, 7}, {2, 4, 6, 7}},
     ------------------------------------------------------------------------
     {{0, 1, 3, 5}, {0, 2, 3, 5}, {0, 2, 4, 5}, {2, 3, 5, 7}, {2, 4, 5, 7},
     ------------------------------------------------------------------------
     {2, 4, 6, 7}}, {{0, 1, 3, 4}, {0, 2, 3, 4}, {1, 3, 4, 7}, {1, 4, 5, 7},
     ------------------------------------------------------------------------
     {2, 3, 4, 6}, {3, 4, 6, 7}}, {{0, 1, 3, 6}, {0, 1, 4, 6}, {0, 2, 3, 6},
     ------------------------------------------------------------------------
     {1, 3, 5, 6}, {1, 4, 5, 6}, {3, 5, 6, 7}}, {{0, 1, 2, 4}, {1, 2, 3, 4},
     ------------------------------------------------------------------------
     {1, 3, 4, 5}, {2, 3, 4, 7}, {2, 4, 6, 7}, {3, 4, 5, 7}}, {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 4}, {0, 3, 4, 5}, {2, 3, 4, 6}, {3, 4, 5, 6}, {3, 5, 6, 7}},
     ------------------------------------------------------------------------
     {{0, 1, 2, 4}, {1, 2, 3, 5}, {1, 2, 4, 5}, {2, 3, 5, 6}, {2, 4, 5, 6},
     ------------------------------------------------------------------------
     {3, 5, 6, 7}}, {{0, 1, 3, 4}, {0, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 6},
     ------------------------------------------------------------------------
     {3, 4, 5, 7}, {3, 4, 6, 7}}, {{0, 1, 2, 6}, {0, 1, 4, 6}, {1, 2, 3, 6},
     ------------------------------------------------------------------------
     {1, 3, 5, 6}, {1, 4, 5, 6}, {3, 5, 6, 7}}, {{0, 1, 2, 6}, {0, 1, 5, 6},
     ------------------------------------------------------------------------
     {0, 4, 5, 6}, {1, 2, 3, 6}, {1, 3, 5, 6}, {3, 5, 6, 7}}, {{0, 1, 2, 4},
     ------------------------------------------------------------------------
     {1, 2, 3, 6}, {1, 2, 4, 6}, {1, 3, 6, 7}, {1, 4, 5, 7}, {1, 4, 6, 7}},
     ------------------------------------------------------------------------
     {{0, 1, 3, 5}, {0, 2, 3, 5}, {0, 2, 5, 6}, {0, 4, 5, 6}, {2, 3, 5, 6},
     ------------------------------------------------------------------------
     {3, 5, 6, 7}}, {{0, 1, 2, 4}, {1, 2, 3, 7}, {1, 2, 4, 6}, {1, 2, 6, 7},
     ------------------------------------------------------------------------
     {1, 4, 5, 7}, {1, 4, 6, 7}}}

o5 : List

i6 : Ts3 = generateTriangulations triangulation(A, T) -- list of Triangulations

o6 = {triangulation {{0, 1, 3, 7}, {0, 1, 5, 7}, {0, 2, 3, 7}, {0, 2, 6, 7},
     ------------------------------------------------------------------------
     {0, 4, 5, 7}, {0, 4, 6, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 5, 7},
     ------------------------------------------------------------------------
     {0, 2, 3, 7}, {0, 2, 4, 7}, {0, 4, 5, 7}, {2, 4, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 3, 5}, {0, 2, 3, 7}, {0, 2, 6, 7}, {0, 3, 5, 7}, {0, 4, 5, 6},
     ------------------------------------------------------------------------
     {0, 5, 6, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 4, 7}, {0, 2, 3, 6},
     ------------------------------------------------------------------------
     {0, 3, 6, 7}, {0, 4, 6, 7}, {1, 4, 5, 7}}, triangulation {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 5, 7}, {0, 3, 6, 7}, {0, 4, 5, 6}, {0, 5, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 2, 5}, {0, 2, 5, 6}, {0, 4, 5, 6}, {1, 2, 3, 5},
     ------------------------------------------------------------------------
     {2, 3, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 3, 4}, {0, 2, 3, 4},
     ------------------------------------------------------------------------
     {1, 3, 4, 5}, {2, 3, 4, 7}, {2, 4, 6, 7}, {3, 4, 5, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 3, 5}, {0, 2, 3, 4}, {0, 3, 4, 5}, {2, 3, 4, 6}, {3, 4, 5, 7},
     ------------------------------------------------------------------------
     {3, 4, 6, 7}}, triangulation {{0, 1, 3, 4}, {0, 2, 3, 6}, {0, 3, 4, 6},
     ------------------------------------------------------------------------
     {1, 3, 4, 5}, {3, 4, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 2, 5},
     ------------------------------------------------------------------------
     {0, 2, 4, 5}, {1, 2, 3, 5}, {2, 3, 5, 6}, {2, 4, 5, 6}, {3, 5, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 2, 4}, {1, 2, 3, 5}, {1, 2, 4, 5}, {2, 3, 5, 7},
     ------------------------------------------------------------------------
     {2, 4, 5, 6}, {2, 5, 6, 7}}, triangulation {{0, 1, 2, 6}, {0, 1, 4, 6},
     ------------------------------------------------------------------------
     {1, 2, 3, 6}, {1, 3, 6, 7}, {1, 4, 5, 6}, {1, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 4}, {1, 2, 3, 4}, {1, 3, 4, 7}, {1, 4, 5, 7}, {2, 3, 4, 7},
     ------------------------------------------------------------------------
     {2, 4, 6, 7}}, triangulation {{0, 1, 3, 6}, {0, 1, 4, 6}, {0, 2, 3, 6},
     ------------------------------------------------------------------------
     {1, 3, 6, 7}, {1, 4, 5, 6}, {1, 5, 6, 7}}, triangulation {{0, 1, 2, 5},
     ------------------------------------------------------------------------
     {0, 2, 4, 5}, {1, 2, 3, 7}, {1, 2, 5, 7}, {2, 4, 5, 6}, {2, 5, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 2, 7}, {0, 1, 5, 7}, {0, 2, 4, 7}, {0, 4, 5, 7},
     ------------------------------------------------------------------------
     {1, 2, 3, 7}, {2, 4, 6, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 4, 7},
     ------------------------------------------------------------------------
     {0, 2, 3, 7}, {0, 2, 6, 7}, {0, 4, 6, 7}, {1, 4, 5, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 3, 5}, {0, 2, 3, 7}, {0, 2, 6, 7}, {0, 3, 5, 7}, {0, 4, 5, 7},
     ------------------------------------------------------------------------
     {0, 4, 6, 7}}, triangulation {{0, 1, 2, 7}, {0, 1, 4, 7}, {0, 2, 4, 7},
     ------------------------------------------------------------------------
     {1, 2, 3, 7}, {1, 4, 5, 7}, {2, 4, 6, 7}}, triangulation {{0, 1, 2, 5},
     ------------------------------------------------------------------------
     {0, 2, 4, 5}, {1, 2, 3, 7}, {1, 2, 5, 7}, {2, 4, 5, 7}, {2, 4, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 2, 5}, {0, 2, 5, 6}, {0, 4, 5, 6}, {1, 2, 3, 7},
     ------------------------------------------------------------------------
     {1, 2, 5, 7}, {2, 5, 6, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 4, 7},
     ------------------------------------------------------------------------
     {0, 2, 3, 7}, {0, 2, 4, 7}, {1, 4, 5, 7}, {2, 4, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 3, 6}, {0, 1, 4, 6}, {0, 2, 3, 6}, {1, 3, 6, 7}, {1, 4, 5, 7},
     ------------------------------------------------------------------------
     {1, 4, 6, 7}}, triangulation {{0, 1, 3, 6}, {0, 1, 5, 6}, {0, 2, 3, 6},
     ------------------------------------------------------------------------
     {0, 4, 5, 6}, {1, 3, 6, 7}, {1, 5, 6, 7}}, triangulation {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 5, 7}, {0, 3, 6, 7}, {0, 4, 5, 7}, {0, 4, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 3, 5}, {0, 2, 3, 5}, {0, 2, 5, 6}, {0, 4, 5, 6},
     ------------------------------------------------------------------------
     {2, 3, 5, 7}, {2, 5, 6, 7}}, triangulation {{0, 1, 2, 4}, {1, 2, 3, 7},
     ------------------------------------------------------------------------
     {1, 2, 4, 5}, {1, 2, 5, 7}, {2, 4, 5, 6}, {2, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 5}, {0, 2, 4, 5}, {1, 2, 3, 5}, {2, 3, 5, 7}, {2, 4, 5, 6},
     ------------------------------------------------------------------------
     {2, 5, 6, 7}}, triangulation {{0, 1, 3, 4}, {0, 2, 3, 6}, {0, 3, 4, 6},
     ------------------------------------------------------------------------
     {1, 3, 4, 5}, {3, 4, 5, 7}, {3, 4, 6, 7}}, triangulation {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 4, 5}, {0, 3, 4, 6}, {3, 4, 5, 6}, {3, 5, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 3, 5}, {0, 2, 3, 5}, {0, 2, 4, 5}, {2, 3, 5, 6},
     ------------------------------------------------------------------------
     {2, 4, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 2, 4}, {1, 2, 3, 6},
     ------------------------------------------------------------------------
     {1, 2, 4, 6}, {1, 3, 5, 6}, {1, 4, 5, 6}, {3, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 4}, {1, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 6}, {3, 4, 5, 6},
     ------------------------------------------------------------------------
     {3, 5, 6, 7}}, triangulation {{0, 1, 2, 4}, {1, 2, 3, 5}, {1, 2, 4, 5},
     ------------------------------------------------------------------------
     {2, 3, 5, 7}, {2, 4, 5, 7}, {2, 4, 6, 7}}, triangulation {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 4}, {0, 3, 4, 5}, {2, 3, 4, 7}, {2, 4, 6, 7}, {3, 4, 5, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 3, 4}, {0, 2, 3, 6}, {0, 3, 4, 6}, {1, 3, 4, 7},
     ------------------------------------------------------------------------
     {1, 4, 5, 7}, {3, 4, 6, 7}}, triangulation {{0, 1, 3, 4}, {0, 2, 3, 4},
     ------------------------------------------------------------------------
     {1, 3, 4, 7}, {1, 4, 5, 7}, {2, 3, 4, 7}, {2, 4, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 6}, {0, 1, 4, 6}, {1, 2, 3, 7}, {1, 2, 6, 7}, {1, 4, 5, 6},
     ------------------------------------------------------------------------
     {1, 5, 6, 7}}, triangulation {{0, 1, 2, 6}, {0, 1, 4, 6}, {1, 2, 3, 6},
     ------------------------------------------------------------------------
     {1, 3, 6, 7}, {1, 4, 5, 7}, {1, 4, 6, 7}}, triangulation {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 5, 6}, {0, 4, 5, 6}, {3, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 4}, {1, 2, 3, 7}, {1, 2, 4, 7}, {1, 4, 5, 7}, {2, 4, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 2, 7}, {0, 1, 5, 7}, {0, 2, 6, 7}, {0, 4, 5, 6},
     ------------------------------------------------------------------------
     {0, 5, 6, 7}, {1, 2, 3, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 5, 7},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 6, 7}, {0, 4, 5, 6}, {0, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 6}, {0, 1, 4, 6}, {1, 2, 3, 7}, {1, 2, 6, 7}, {1, 4, 5, 7},
     ------------------------------------------------------------------------
     {1, 4, 6, 7}}, triangulation {{0, 1, 2, 4}, {1, 2, 3, 4}, {1, 3, 4, 7},
     ------------------------------------------------------------------------
     {1, 4, 5, 7}, {2, 3, 4, 6}, {3, 4, 6, 7}}, triangulation {{0, 1, 2, 4},
     ------------------------------------------------------------------------
     {1, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 6}, {3, 4, 5, 7}, {3, 4, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 3, 4}, {0, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 6},
     ------------------------------------------------------------------------
     {3, 4, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 2, 4}, {1, 2, 3, 6},
     ------------------------------------------------------------------------
     {1, 2, 4, 6}, {1, 3, 6, 7}, {1, 4, 5, 6}, {1, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 4}, {1, 2, 3, 7}, {1, 2, 4, 6}, {1, 2, 6, 7}, {1, 4, 5, 6},
     ------------------------------------------------------------------------
     {1, 5, 6, 7}}, triangulation {{0, 1, 3, 5}, {0, 2, 3, 5}, {0, 2, 4, 5},
     ------------------------------------------------------------------------
     {2, 3, 5, 7}, {2, 4, 5, 6}, {2, 5, 6, 7}}, triangulation {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 4, 5}, {0, 3, 4, 6}, {3, 4, 5, 7}, {3, 4, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 3, 6}, {0, 1, 5, 6}, {0, 2, 3, 6}, {0, 4, 5, 6},
     ------------------------------------------------------------------------
     {1, 3, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 2, 5}, {0, 2, 5, 6},
     ------------------------------------------------------------------------
     {0, 4, 5, 6}, {1, 2, 3, 5}, {2, 3, 5, 7}, {2, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 5}, {0, 2, 4, 5}, {1, 2, 3, 5}, {2, 3, 5, 7}, {2, 4, 5, 7},
     ------------------------------------------------------------------------
     {2, 4, 6, 7}}, triangulation {{0, 1, 2, 4}, {1, 2, 3, 7}, {1, 2, 4, 5},
     ------------------------------------------------------------------------
     {1, 2, 5, 7}, {2, 4, 5, 7}, {2, 4, 6, 7}}, triangulation {{0, 1, 2, 6},
     ------------------------------------------------------------------------
     {0, 1, 5, 6}, {0, 4, 5, 6}, {1, 2, 3, 6}, {1, 3, 6, 7}, {1, 5, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 2, 7}, {0, 1, 5, 7}, {0, 2, 6, 7}, {0, 4, 5, 7},
     ------------------------------------------------------------------------
     {0, 4, 6, 7}, {1, 2, 3, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 5, 7},
     ------------------------------------------------------------------------
     {0, 2, 3, 7}, {0, 2, 6, 7}, {0, 4, 5, 6}, {0, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 7}, {0, 1, 4, 7}, {0, 2, 6, 7}, {0, 4, 6, 7}, {1, 2, 3, 7},
     ------------------------------------------------------------------------
     {1, 4, 5, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 5, 7}, {0, 2, 3, 6},
     ------------------------------------------------------------------------
     {0, 3, 6, 7}, {0, 4, 5, 7}, {0, 4, 6, 7}}, triangulation {{0, 1, 2, 6},
     ------------------------------------------------------------------------
     {0, 1, 5, 6}, {0, 4, 5, 6}, {1, 2, 3, 7}, {1, 2, 6, 7}, {1, 5, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 3, 5}, {0, 2, 3, 7}, {0, 2, 4, 7}, {0, 3, 5, 7},
     ------------------------------------------------------------------------
     {0, 4, 5, 7}, {2, 4, 6, 7}}, triangulation {{0, 1, 3, 5}, {0, 2, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 4, 5}, {2, 3, 5, 7}, {2, 4, 5, 7}, {2, 4, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 3, 4}, {0, 2, 3, 4}, {1, 3, 4, 7}, {1, 4, 5, 7}, {2, 3, 4, 6},
     ------------------------------------------------------------------------
     {3, 4, 6, 7}}, triangulation {{0, 1, 3, 6}, {0, 1, 4, 6}, {0, 2, 3, 6},
     ------------------------------------------------------------------------
     {1, 3, 5, 6}, {1, 4, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 2, 4},
     ------------------------------------------------------------------------
     {1, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 7}, {2, 4, 6, 7}, {3, 4, 5, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 3, 5}, {0, 2, 3, 4}, {0, 3, 4, 5}, {2, 3, 4, 6},
     ------------------------------------------------------------------------
     {3, 4, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 2, 4}, {1, 2, 3, 5},
     ------------------------------------------------------------------------
     {1, 2, 4, 5}, {2, 3, 5, 6}, {2, 4, 5, 6}, {3, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 3, 4}, {0, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 6}, {3, 4, 5, 7},
     ------------------------------------------------------------------------
     {3, 4, 6, 7}}, triangulation {{0, 1, 2, 6}, {0, 1, 4, 6}, {1, 2, 3, 6},
     ------------------------------------------------------------------------
     {1, 3, 5, 6}, {1, 4, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 2, 6},
     ------------------------------------------------------------------------
     {0, 1, 5, 6}, {0, 4, 5, 6}, {1, 2, 3, 6}, {1, 3, 5, 6}, {3, 5, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 2, 4}, {1, 2, 3, 6}, {1, 2, 4, 6}, {1, 3, 6, 7},
     ------------------------------------------------------------------------
     {1, 4, 5, 7}, {1, 4, 6, 7}}, triangulation {{0, 1, 3, 5}, {0, 2, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 5, 6}, {0, 4, 5, 6}, {2, 3, 5, 6}, {3, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 4}, {1, 2, 3, 7}, {1, 2, 4, 6}, {1, 2, 6, 7}, {1, 4, 5, 7},
     ------------------------------------------------------------------------
     {1, 4, 6, 7}}}

o6 : List

i7 : Ts4 = generateTriangulations tri -- list of Triangulations

o7 = {triangulation {{0, 1, 3, 7}, {0, 1, 5, 7}, {0, 2, 3, 7}, {0, 2, 6, 7},
     ------------------------------------------------------------------------
     {0, 4, 5, 7}, {0, 4, 6, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 5, 7},
     ------------------------------------------------------------------------
     {0, 2, 3, 7}, {0, 2, 4, 7}, {0, 4, 5, 7}, {2, 4, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 3, 5}, {0, 2, 3, 7}, {0, 2, 6, 7}, {0, 3, 5, 7}, {0, 4, 5, 6},
     ------------------------------------------------------------------------
     {0, 5, 6, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 4, 7}, {0, 2, 3, 6},
     ------------------------------------------------------------------------
     {0, 3, 6, 7}, {0, 4, 6, 7}, {1, 4, 5, 7}}, triangulation {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 5, 7}, {0, 3, 6, 7}, {0, 4, 5, 6}, {0, 5, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 2, 5}, {0, 2, 5, 6}, {0, 4, 5, 6}, {1, 2, 3, 5},
     ------------------------------------------------------------------------
     {2, 3, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 3, 4}, {0, 2, 3, 4},
     ------------------------------------------------------------------------
     {1, 3, 4, 5}, {2, 3, 4, 7}, {2, 4, 6, 7}, {3, 4, 5, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 3, 5}, {0, 2, 3, 4}, {0, 3, 4, 5}, {2, 3, 4, 6}, {3, 4, 5, 7},
     ------------------------------------------------------------------------
     {3, 4, 6, 7}}, triangulation {{0, 1, 3, 4}, {0, 2, 3, 6}, {0, 3, 4, 6},
     ------------------------------------------------------------------------
     {1, 3, 4, 5}, {3, 4, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 2, 5},
     ------------------------------------------------------------------------
     {0, 2, 4, 5}, {1, 2, 3, 5}, {2, 3, 5, 6}, {2, 4, 5, 6}, {3, 5, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 2, 4}, {1, 2, 3, 5}, {1, 2, 4, 5}, {2, 3, 5, 7},
     ------------------------------------------------------------------------
     {2, 4, 5, 6}, {2, 5, 6, 7}}, triangulation {{0, 1, 2, 6}, {0, 1, 4, 6},
     ------------------------------------------------------------------------
     {1, 2, 3, 6}, {1, 3, 6, 7}, {1, 4, 5, 6}, {1, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 4}, {1, 2, 3, 4}, {1, 3, 4, 7}, {1, 4, 5, 7}, {2, 3, 4, 7},
     ------------------------------------------------------------------------
     {2, 4, 6, 7}}, triangulation {{0, 1, 3, 6}, {0, 1, 4, 6}, {0, 2, 3, 6},
     ------------------------------------------------------------------------
     {1, 3, 6, 7}, {1, 4, 5, 6}, {1, 5, 6, 7}}, triangulation {{0, 1, 2, 5},
     ------------------------------------------------------------------------
     {0, 2, 4, 5}, {1, 2, 3, 7}, {1, 2, 5, 7}, {2, 4, 5, 6}, {2, 5, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 2, 7}, {0, 1, 5, 7}, {0, 2, 4, 7}, {0, 4, 5, 7},
     ------------------------------------------------------------------------
     {1, 2, 3, 7}, {2, 4, 6, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 4, 7},
     ------------------------------------------------------------------------
     {0, 2, 3, 7}, {0, 2, 6, 7}, {0, 4, 6, 7}, {1, 4, 5, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 3, 5}, {0, 2, 3, 7}, {0, 2, 6, 7}, {0, 3, 5, 7}, {0, 4, 5, 7},
     ------------------------------------------------------------------------
     {0, 4, 6, 7}}, triangulation {{0, 1, 2, 7}, {0, 1, 4, 7}, {0, 2, 4, 7},
     ------------------------------------------------------------------------
     {1, 2, 3, 7}, {1, 4, 5, 7}, {2, 4, 6, 7}}, triangulation {{0, 1, 2, 5},
     ------------------------------------------------------------------------
     {0, 2, 4, 5}, {1, 2, 3, 7}, {1, 2, 5, 7}, {2, 4, 5, 7}, {2, 4, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 2, 5}, {0, 2, 5, 6}, {0, 4, 5, 6}, {1, 2, 3, 7},
     ------------------------------------------------------------------------
     {1, 2, 5, 7}, {2, 5, 6, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 4, 7},
     ------------------------------------------------------------------------
     {0, 2, 3, 7}, {0, 2, 4, 7}, {1, 4, 5, 7}, {2, 4, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 3, 6}, {0, 1, 4, 6}, {0, 2, 3, 6}, {1, 3, 6, 7}, {1, 4, 5, 7},
     ------------------------------------------------------------------------
     {1, 4, 6, 7}}, triangulation {{0, 1, 3, 6}, {0, 1, 5, 6}, {0, 2, 3, 6},
     ------------------------------------------------------------------------
     {0, 4, 5, 6}, {1, 3, 6, 7}, {1, 5, 6, 7}}, triangulation {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 5, 7}, {0, 3, 6, 7}, {0, 4, 5, 7}, {0, 4, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 3, 5}, {0, 2, 3, 5}, {0, 2, 5, 6}, {0, 4, 5, 6},
     ------------------------------------------------------------------------
     {2, 3, 5, 7}, {2, 5, 6, 7}}, triangulation {{0, 1, 2, 4}, {1, 2, 3, 7},
     ------------------------------------------------------------------------
     {1, 2, 4, 5}, {1, 2, 5, 7}, {2, 4, 5, 6}, {2, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 5}, {0, 2, 4, 5}, {1, 2, 3, 5}, {2, 3, 5, 7}, {2, 4, 5, 6},
     ------------------------------------------------------------------------
     {2, 5, 6, 7}}, triangulation {{0, 1, 3, 4}, {0, 2, 3, 6}, {0, 3, 4, 6},
     ------------------------------------------------------------------------
     {1, 3, 4, 5}, {3, 4, 5, 7}, {3, 4, 6, 7}}, triangulation {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 4, 5}, {0, 3, 4, 6}, {3, 4, 5, 6}, {3, 5, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 3, 5}, {0, 2, 3, 5}, {0, 2, 4, 5}, {2, 3, 5, 6},
     ------------------------------------------------------------------------
     {2, 4, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 2, 4}, {1, 2, 3, 6},
     ------------------------------------------------------------------------
     {1, 2, 4, 6}, {1, 3, 5, 6}, {1, 4, 5, 6}, {3, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 4}, {1, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 6}, {3, 4, 5, 6},
     ------------------------------------------------------------------------
     {3, 5, 6, 7}}, triangulation {{0, 1, 2, 4}, {1, 2, 3, 5}, {1, 2, 4, 5},
     ------------------------------------------------------------------------
     {2, 3, 5, 7}, {2, 4, 5, 7}, {2, 4, 6, 7}}, triangulation {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 4}, {0, 3, 4, 5}, {2, 3, 4, 7}, {2, 4, 6, 7}, {3, 4, 5, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 3, 4}, {0, 2, 3, 6}, {0, 3, 4, 6}, {1, 3, 4, 7},
     ------------------------------------------------------------------------
     {1, 4, 5, 7}, {3, 4, 6, 7}}, triangulation {{0, 1, 3, 4}, {0, 2, 3, 4},
     ------------------------------------------------------------------------
     {1, 3, 4, 7}, {1, 4, 5, 7}, {2, 3, 4, 7}, {2, 4, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 6}, {0, 1, 4, 6}, {1, 2, 3, 7}, {1, 2, 6, 7}, {1, 4, 5, 6},
     ------------------------------------------------------------------------
     {1, 5, 6, 7}}, triangulation {{0, 1, 2, 6}, {0, 1, 4, 6}, {1, 2, 3, 6},
     ------------------------------------------------------------------------
     {1, 3, 6, 7}, {1, 4, 5, 7}, {1, 4, 6, 7}}, triangulation {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 5, 6}, {0, 4, 5, 6}, {3, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 4}, {1, 2, 3, 7}, {1, 2, 4, 7}, {1, 4, 5, 7}, {2, 4, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 2, 7}, {0, 1, 5, 7}, {0, 2, 6, 7}, {0, 4, 5, 6},
     ------------------------------------------------------------------------
     {0, 5, 6, 7}, {1, 2, 3, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 5, 7},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 6, 7}, {0, 4, 5, 6}, {0, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 6}, {0, 1, 4, 6}, {1, 2, 3, 7}, {1, 2, 6, 7}, {1, 4, 5, 7},
     ------------------------------------------------------------------------
     {1, 4, 6, 7}}, triangulation {{0, 1, 2, 4}, {1, 2, 3, 4}, {1, 3, 4, 7},
     ------------------------------------------------------------------------
     {1, 4, 5, 7}, {2, 3, 4, 6}, {3, 4, 6, 7}}, triangulation {{0, 1, 2, 4},
     ------------------------------------------------------------------------
     {1, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 6}, {3, 4, 5, 7}, {3, 4, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 3, 4}, {0, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 6},
     ------------------------------------------------------------------------
     {3, 4, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 2, 4}, {1, 2, 3, 6},
     ------------------------------------------------------------------------
     {1, 2, 4, 6}, {1, 3, 6, 7}, {1, 4, 5, 6}, {1, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 4}, {1, 2, 3, 7}, {1, 2, 4, 6}, {1, 2, 6, 7}, {1, 4, 5, 6},
     ------------------------------------------------------------------------
     {1, 5, 6, 7}}, triangulation {{0, 1, 3, 5}, {0, 2, 3, 5}, {0, 2, 4, 5},
     ------------------------------------------------------------------------
     {2, 3, 5, 7}, {2, 4, 5, 6}, {2, 5, 6, 7}}, triangulation {{0, 1, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 3, 6}, {0, 3, 4, 5}, {0, 3, 4, 6}, {3, 4, 5, 7}, {3, 4, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 3, 6}, {0, 1, 5, 6}, {0, 2, 3, 6}, {0, 4, 5, 6},
     ------------------------------------------------------------------------
     {1, 3, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 2, 5}, {0, 2, 5, 6},
     ------------------------------------------------------------------------
     {0, 4, 5, 6}, {1, 2, 3, 5}, {2, 3, 5, 7}, {2, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 5}, {0, 2, 4, 5}, {1, 2, 3, 5}, {2, 3, 5, 7}, {2, 4, 5, 7},
     ------------------------------------------------------------------------
     {2, 4, 6, 7}}, triangulation {{0, 1, 2, 4}, {1, 2, 3, 7}, {1, 2, 4, 5},
     ------------------------------------------------------------------------
     {1, 2, 5, 7}, {2, 4, 5, 7}, {2, 4, 6, 7}}, triangulation {{0, 1, 2, 6},
     ------------------------------------------------------------------------
     {0, 1, 5, 6}, {0, 4, 5, 6}, {1, 2, 3, 6}, {1, 3, 6, 7}, {1, 5, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 2, 7}, {0, 1, 5, 7}, {0, 2, 6, 7}, {0, 4, 5, 7},
     ------------------------------------------------------------------------
     {0, 4, 6, 7}, {1, 2, 3, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 5, 7},
     ------------------------------------------------------------------------
     {0, 2, 3, 7}, {0, 2, 6, 7}, {0, 4, 5, 6}, {0, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 7}, {0, 1, 4, 7}, {0, 2, 6, 7}, {0, 4, 6, 7}, {1, 2, 3, 7},
     ------------------------------------------------------------------------
     {1, 4, 5, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 5, 7}, {0, 2, 3, 6},
     ------------------------------------------------------------------------
     {0, 3, 6, 7}, {0, 4, 5, 7}, {0, 4, 6, 7}}, triangulation {{0, 1, 2, 6},
     ------------------------------------------------------------------------
     {0, 1, 5, 6}, {0, 4, 5, 6}, {1, 2, 3, 7}, {1, 2, 6, 7}, {1, 5, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 3, 5}, {0, 2, 3, 7}, {0, 2, 4, 7}, {0, 3, 5, 7},
     ------------------------------------------------------------------------
     {0, 4, 5, 7}, {2, 4, 6, 7}}, triangulation {{0, 1, 3, 5}, {0, 2, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 4, 5}, {2, 3, 5, 7}, {2, 4, 5, 7}, {2, 4, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 3, 4}, {0, 2, 3, 4}, {1, 3, 4, 7}, {1, 4, 5, 7}, {2, 3, 4, 6},
     ------------------------------------------------------------------------
     {3, 4, 6, 7}}, triangulation {{0, 1, 3, 6}, {0, 1, 4, 6}, {0, 2, 3, 6},
     ------------------------------------------------------------------------
     {1, 3, 5, 6}, {1, 4, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 2, 4},
     ------------------------------------------------------------------------
     {1, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 7}, {2, 4, 6, 7}, {3, 4, 5, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 3, 5}, {0, 2, 3, 4}, {0, 3, 4, 5}, {2, 3, 4, 6},
     ------------------------------------------------------------------------
     {3, 4, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 2, 4}, {1, 2, 3, 5},
     ------------------------------------------------------------------------
     {1, 2, 4, 5}, {2, 3, 5, 6}, {2, 4, 5, 6}, {3, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 3, 4}, {0, 2, 3, 4}, {1, 3, 4, 5}, {2, 3, 4, 6}, {3, 4, 5, 7},
     ------------------------------------------------------------------------
     {3, 4, 6, 7}}, triangulation {{0, 1, 2, 6}, {0, 1, 4, 6}, {1, 2, 3, 6},
     ------------------------------------------------------------------------
     {1, 3, 5, 6}, {1, 4, 5, 6}, {3, 5, 6, 7}}, triangulation {{0, 1, 2, 6},
     ------------------------------------------------------------------------
     {0, 1, 5, 6}, {0, 4, 5, 6}, {1, 2, 3, 6}, {1, 3, 5, 6}, {3, 5, 6, 7}},
     ------------------------------------------------------------------------
     triangulation {{0, 1, 2, 4}, {1, 2, 3, 6}, {1, 2, 4, 6}, {1, 3, 6, 7},
     ------------------------------------------------------------------------
     {1, 4, 5, 7}, {1, 4, 6, 7}}, triangulation {{0, 1, 3, 5}, {0, 2, 3, 5},
     ------------------------------------------------------------------------
     {0, 2, 5, 6}, {0, 4, 5, 6}, {2, 3, 5, 6}, {3, 5, 6, 7}}, triangulation
     ------------------------------------------------------------------------
     {{0, 1, 2, 4}, {1, 2, 3, 7}, {1, 2, 4, 6}, {1, 2, 6, 7}, {1, 4, 5, 7},
     ------------------------------------------------------------------------
     {1, 4, 6, 7}}}

o7 : List

i8 : all(Ts4, isFine)

o8 = true

i9 : all(Ts4, isStar)

o9 = false

i10 : all(Ts4, isRegularTriangulation)

o10 = true

i11 : Ts4/isStar//tally

o11 = Tally{false => 66}
            true => 8

o11 : Tally

i12 : Ts4/gkzVector

           8  8  8  8  8  8       20  8     8     8  4          4  8     4 
o12 = {{8, -, -, -, -, -, -, 8}, {--, -, 4, -, 4, -, -, 8}, {8, -, -, 4, -,
           3  3  3  3  3  3        3  3     3     3  3          3  3     3 
      -----------------------------------------------------------------------
      16     16    20     4        4     20       4  4  16  4  16  16     
      --, 4, --}, {--, 4, -, 4, 4, -, 4, --}, {8, -, -, --, -, --, --, 4},
       3      3     3     3        3      3       3  3   3  3   3   3     
      -----------------------------------------------------------------------
          8  16     4     16  4    8  8     20     8  4          4  8     20 
      {4, -, --, 4, -, 8, --, -}, {-, -, 4, --, 8, -, -, 4}, {4, -, -, 8, --,
          3   3     3      3  3    3  3      3     3  3          3  3      3 
      -----------------------------------------------------------------------
         8  8       8  4     16     16  4    8  8  20     8        4    4    
      4, -, -}, {4, -, -, 8, --, 4, --, -}, {-, -, --, 4, -, 8, 4, -}, {-, 4,
         3  3       3  3      3      3  3    3  3   3     3        3    3    
      -----------------------------------------------------------------------
         8     20  8  8    8     8  8  8  8     8    4  16  16        4  4 
      8, -, 4, --, -, -}, {-, 8, -, -, -, -, 8, -}, {-, --, --, 4, 8, -, -,
         3      3  3  3    3     3  3  3  3     3    3   3   3        3  3 
      -----------------------------------------------------------------------
      16       20  4     8  8     8    8        4  8  20  8       16     16 
      --}, {4, --, -, 4, -, -, 8, -}, {-, 4, 8, -, -, --, -, 4}, {--, 4, --,
       3        3  3     3  3     3    3        3  3   3  3        3      3 
      -----------------------------------------------------------------------
      4     8  4       20     8  8     4  8          4  8     8     8  20  
      -, 4, -, -, 8}, {--, 4, -, -, 4, -, -, 8}, {8, -, -, 4, -, 4, -, --},
      3     3  3        3     3  3     3  3          3  3     3     3   3  
      -----------------------------------------------------------------------
          16  16  4  16  4  4       8        4     16  4  16          20  4 
      {4, --, --, -, --, -, -, 8}, {-, 4, 8, -, 4, --, -, --}, {4, 4, --, -,
           3   3  3   3  3  3       3        3      3  3   3           3  3 
      -----------------------------------------------------------------------
      4  20          16        8  16  4  4          20  4        4  20     
      -, --, 4, 4}, {--, 4, 4, -, --, -, -, 8}, {4, --, -, 4, 4, -, --, 4},
      3   3           3        3   3  3  3           3  3        3   3     
      -----------------------------------------------------------------------
       16  16  4     4        8       4  4  16  8        16    16  4  16    
      {--, --, -, 4, -, 4, 8, -}, {8, -, -, --, -, 4, 4, --}, {--, -, --, 4,
        3   3  3     3        3       3  3   3  3         3     3  3   3    
      -----------------------------------------------------------------------
      4        8    4  16     4     16  8       8  8     8  8     8  8      
      -, 8, 4, -}, {-, --, 8, -, 4, --, -, 4}, {-, -, 8, -, -, 8, -, -}, {4,
      3        3    3   3     3      3  3       3  3     3  3     3  3      
      -----------------------------------------------------------------------
      8  4     20  8     8    16  4  4        16  16  4       4  16  16  8 
      -, -, 8, --, -, 4, -}, {--, -, -, 8, 4, --, --, -}, {4, -, --, --, -,
      3  3      3  3     3     3  3  3         3   3  3       3   3   3  3 
      -----------------------------------------------------------------------
            4    4  20              20  4    4        20  20        4    4 
      8, 4, -}, {-, --, 4, 4, 4, 4, --, -}, {-, 4, 4, --, --, 4, 4, -}, {-,
            3    3   3               3  3    3         3   3        3    3 
      -----------------------------------------------------------------------
            8  16  16  4          4     20  20     4             4  20  20 
      4, 8, -, --, --, -, 4}, {4, -, 4, --, --, 4, -, 4}, {4, 4, -, --, --,
            3   3   3  3          3      3   3     3             3   3   3 
      -----------------------------------------------------------------------
      4          8        16     4  4  16    8        4  8  8  20       8    
      -, 4, 4}, {-, 4, 4, --, 8, -, -, --}, {-, 8, 4, -, -, -, --, 4}, {-, 8,
      3          3         3     3  3   3    3        3  3  3   3       3    
      -----------------------------------------------------------------------
      8  8     4  20       20  4  4  20  4  20  20  4    4  20  20  4  20  4 
      -, -, 4, -, --, 4}, {--, -, -, --, -, --, --, -}, {-, --, --, -, --, -,
      3  3     3   3        3  3  3   3  3   3   3  3    3   3   3  3   3  3 
      -----------------------------------------------------------------------
      4  20    20        4  4        20       8  4     4     16  16    8    
      -, --}, {--, 4, 4, -, -, 4, 4, --}, {8, -, -, 4, -, 4, --, --}, {-, 8,
      3   3     3        3  3         3       3  3     3      3   3    3    
      -----------------------------------------------------------------------
         4     4  16  16    4  16     16     4  8       4        20     8  8 
      4, -, 4, -, --, --}, {-, --, 4, --, 8, -, -, 4}, {-, 4, 4, --, 8, -, -,
         3     3   3   3    3   3      3     3  3       3         3     3  3 
      -----------------------------------------------------------------------
      8    8  8  8     20        4    4        8     8  20  8    4     16  4 
      -}, {-, -, -, 8, --, 4, 4, -}, {-, 8, 4, -, 4, -, --, -}, {-, 8, --, -,
      3    3  3  3      3        3    3        3     3   3  3    3      3  3 
      -----------------------------------------------------------------------
         8  16          4  20     8     8  8    16  4  4     16        8  
      4, -, --, 4}, {4, -, --, 4, -, 8, -, -}, {--, -, -, 8, --, 4, 4, -},
         3   3          3   3     3     3  3     3  3  3      3        3  
      -----------------------------------------------------------------------
       16     4  16  4  16     4       8  20  8  4        8    8  8     8    
      {--, 4, -, --, -, --, 8, -}, {4, -, --, -, -, 8, 4, -}, {-, -, 8, -, 4,
        3     3   3  3   3     3       3   3  3  3        3    3  3     3    
      -----------------------------------------------------------------------
      20  4       4  16     4  16     4  16       20  8  8  4        8    20 
      --, -, 4}, {-, --, 8, -, --, 4, -, --}, {4, --, -, -, -, 4, 8, -}, {--,
       3  3       3   3     3   3     3   3        3  3  3  3        3     3 
      -----------------------------------------------------------------------
            4  8  8  8          8  8  8  4        20    16  16     4     4 
      4, 4, -, -, -, -, 8}, {8, -, -, -, -, 4, 4, --}, {--, --, 4, -, 4, -,
            3  3  3  3          3  3  3  3         3     3   3     3     3 
      -----------------------------------------------------------------------
      8          8  4     8  8     20       20     4  4     20       20  4 
      -, 8}, {8, -, -, 4, -, -, 4, --}, {4, --, 4, -, -, 4, --, 4}, {--, -,
      3          3  3     3  3      3        3     3  3      3        3  3 
      -----------------------------------------------------------------------
                  4  20       4  20        20  4       8     8  20     4  8 
      4, 4, 4, 4, -, --}, {4, -, --, 4, 4, --, -, 4}, {-, 4, -, --, 8, -, -,
                  3   3       3   3         3  3       3     3   3     3  3 
      -----------------------------------------------------------------------
              16  4  16  8        4    4     16  16     8  4          4  8 
      4}, {4, --, -, --, -, 4, 8, -}, {-, 4, --, --, 8, -, -, 4}, {4, -, -,
               3  3   3  3        3    3      3   3     3  3          3  3 
      -----------------------------------------------------------------------
         16  16     4    4     20        20     4    8  8  8        8  8  8  
      8, --, --, 4, -}, {-, 4, --, 4, 4, --, 4, -}, {-, -, -, 8, 8, -, -, -},
          3   3     3    3      3         3     3    3  3  3        3  3  3  
      -----------------------------------------------------------------------
       8  20  8     8        4       16  8     4  16     4    4        8  16 
      {-, --, -, 4, -, 4, 8, -}, {4, --, -, 4, -, --, 8, -}, {-, 8, 4, -, --,
       3   3  3     3        3        3  3     3   3     3    3        3   3 
      -----------------------------------------------------------------------
      4  16       16  4     16  4     16  4    4     16  4  16  4     16
      -, --, 4}, {--, -, 4, --, -, 8, --, -}, {-, 8, --, -, --, -, 4, --}}
      3   3        3  3      3  3      3  3    3      3  3   3  3      3

o12 : List

i13 : volume convexHull A -- 8

o13 = 8

o13 : QQ

i14 : stars1 = select(Ts4, t -> (gkzVector t)#-1 == 8)

o14 = {triangulation {{0, 1, 3, 7}, {0, 1, 5, 7}, {0, 2, 3, 7}, {0, 2, 6, 7},
      -----------------------------------------------------------------------
      {0, 4, 5, 7}, {0, 4, 6, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 5, 7},
      -----------------------------------------------------------------------
      {0, 2, 3, 7}, {0, 2, 4, 7}, {0, 4, 5, 7}, {2, 4, 6, 7}}, triangulation
      -----------------------------------------------------------------------
      {{0, 1, 2, 7}, {0, 1, 5, 7}, {0, 2, 4, 7}, {0, 4, 5, 7}, {1, 2, 3, 7},
      -----------------------------------------------------------------------
      {2, 4, 6, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 4, 7}, {0, 2, 3, 7},
      -----------------------------------------------------------------------
      {0, 2, 6, 7}, {0, 4, 6, 7}, {1, 4, 5, 7}}, triangulation {{0, 1, 2, 7},
      -----------------------------------------------------------------------
      {0, 1, 4, 7}, {0, 2, 4, 7}, {1, 2, 3, 7}, {1, 4, 5, 7}, {2, 4, 6, 7}},
      -----------------------------------------------------------------------
      triangulation {{0, 1, 3, 7}, {0, 1, 4, 7}, {0, 2, 3, 7}, {0, 2, 4, 7},
      -----------------------------------------------------------------------
      {1, 4, 5, 7}, {2, 4, 6, 7}}, triangulation {{0, 1, 2, 7}, {0, 1, 5, 7},
      -----------------------------------------------------------------------
      {0, 2, 6, 7}, {0, 4, 5, 7}, {0, 4, 6, 7}, {1, 2, 3, 7}}, triangulation
      -----------------------------------------------------------------------
      {{0, 1, 2, 7}, {0, 1, 4, 7}, {0, 2, 6, 7}, {0, 4, 6, 7}, {1, 2, 3, 7},
      -----------------------------------------------------------------------
      {1, 4, 5, 7}}}

o14 : List

i15 : stars2 = select(Ts4, isStar)

o15 = {triangulation {{0, 1, 3, 7}, {0, 1, 5, 7}, {0, 2, 3, 7}, {0, 2, 6, 7},
      -----------------------------------------------------------------------
      {0, 4, 5, 7}, {0, 4, 6, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 5, 7},
      -----------------------------------------------------------------------
      {0, 2, 3, 7}, {0, 2, 4, 7}, {0, 4, 5, 7}, {2, 4, 6, 7}}, triangulation
      -----------------------------------------------------------------------
      {{0, 1, 2, 7}, {0, 1, 5, 7}, {0, 2, 4, 7}, {0, 4, 5, 7}, {1, 2, 3, 7},
      -----------------------------------------------------------------------
      {2, 4, 6, 7}}, triangulation {{0, 1, 3, 7}, {0, 1, 4, 7}, {0, 2, 3, 7},
      -----------------------------------------------------------------------
      {0, 2, 6, 7}, {0, 4, 6, 7}, {1, 4, 5, 7}}, triangulation {{0, 1, 2, 7},
      -----------------------------------------------------------------------
      {0, 1, 4, 7}, {0, 2, 4, 7}, {1, 2, 3, 7}, {1, 4, 5, 7}, {2, 4, 6, 7}},
      -----------------------------------------------------------------------
      triangulation {{0, 1, 3, 7}, {0, 1, 4, 7}, {0, 2, 3, 7}, {0, 2, 4, 7},
      -----------------------------------------------------------------------
      {1, 4, 5, 7}, {2, 4, 6, 7}}, triangulation {{0, 1, 2, 7}, {0, 1, 5, 7},
      -----------------------------------------------------------------------
      {0, 2, 6, 7}, {0, 4, 5, 7}, {0, 4, 6, 7}, {1, 2, 3, 7}}, triangulation
      -----------------------------------------------------------------------
      {{0, 1, 2, 7}, {0, 1, 4, 7}, {0, 2, 6, 7}, {0, 4, 6, 7}, {1, 2, 3, 7},
      -----------------------------------------------------------------------
      {1, 4, 5, 7}}}

o15 : List

i16 : stars1 == stars2

o16 = true

Caveat

This function is written in the top level Macaulay2 language, and so is much slower than allTriangulations, which calls the topcom code written in C++. On the other hand, one can give this function a limit for the number of triangulations to generate, so can be used to generate triangulations in the case when the number is too large to write down all of them.

Ways to use generateTriangulations:

generateTriangulations(Matrix)
generateTriangulations(Matrix,List) (missing documentation)
generateTriangulations(Triangulation) (missing documentation)

For the programmer