next | previous | forward | backward | up | index | toc

# generateTriangulations -- generate all triangulations with certain properties

## Synopsis

• Usage:
Ts = generateTriangulations A
Ts = generateTriangulations(A, tri)
Ts = generateTriangulations T
• Inputs:
• A, , 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 => , default value false, Only generate regular triangulations
• Homogenize => , 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, 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}}, 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}}} o4 : List i5 : Ts2 = generateTriangulations(A, T) -- list of list of subsets o5 = {{{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}}, {{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}}} o5 : List i6 : Ts3 = generateTriangulations triangulation(A, T) -- list of Triangulations o6 = {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}}, 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}}} o6 : List i7 : Ts4 = generateTriangulations tri -- list of Triangulations o7 = {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}}, 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}}} 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 20 4 4 20 8 4 4 16 16 8 4 o12 = {{--, 4, 4, -, -, 4, 4, --}, {8, -, -, 4, -, 4, --, --}, {-, 8, 4, -, 3 3 3 3 3 3 3 3 3 3 3 ----------------------------------------------------------------------- 4 16 16 4 16 16 4 8 4 20 8 8 8 4, -, --, --}, {-, --, 4, --, 8, -, -, 4}, {-, 4, 4, --, 8, -, -, -}, 3 3 3 3 3 3 3 3 3 3 3 3 3 ----------------------------------------------------------------------- 8 8 8 20 4 4 8 8 20 8 4 16 4 {-, -, -, 8, --, 4, 4, -}, {-, 8, 4, -, 4, -, --, -}, {-, 8, --, -, 4, 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 16 -, --, 4}, {4, -, --, 4, -, 8, -, -}, {--, -, -, 8, --, 4, 4, -}, {--, 3 3 3 3 3 3 3 3 3 3 3 3 3 ----------------------------------------------------------------------- 4 16 4 16 4 8 20 8 4 8 8 8 8 20 4, -, --, -, --, 8, -}, {4, -, --, -, -, 8, 4, -}, {-, -, 8, -, 4, --, 3 3 3 3 3 3 3 3 3 3 3 3 3 3 ----------------------------------------------------------------------- 4 4 16 4 16 4 16 20 8 8 4 8 20 -, 4}, {-, --, 8, -, --, 4, -, --}, {4, --, -, -, -, 4, 8, -}, {--, 4, 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 8 4, -, -, -, -, 8}, {8, -, -, -, -, 4, 4, --}, {--, --, 4, -, 4, -, -, 3 3 3 3 3 3 3 3 3 3 3 3 3 3 ----------------------------------------------------------------------- 8 4 8 8 20 20 4 4 20 20 4 8}, {8, -, -, 4, -, -, 4, --}, {4, --, 4, -, -, 4, --, 4}, {--, -, 4, 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, -, --, 8, -, -, 4}, 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, 8, -}, {-, 4, --, --, 8, -, -, 4}, {4, -, -, 8, 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 --, --, 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 ----------------------------------------------------------------------- 8 8 8 8 8 8 20 8 8 8 4 4 8 4 {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 -, --}} 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, 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}}, 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}}} o14 : List i15 : stars2 = select(Ts4, isStar) o15 = {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}}, 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}}} 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.