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

# polyhedra -- computes all polyhedra of a polyhedral complex of a certain dimension

## Synopsis

• Usage:
L = polyhedra(d,PC)
• Inputs:
• Outputs:

## Description

polyhedra computes the List of all Polyhedra in PC of dimension d.
 i1 : PC = polyhedralComplex hypercube 3 o1 = PC o1 : PolyhedralComplex i2 : L = polyhedra(2,PC) o2 = {({0, 1}, {}), ({0, 2}, {}), ({0, 4}, {}), ({1, 3}, {}), ({1, 5}, {}), ------------------------------------------------------------------------ ({2, 3}, {}), ({2, 6}, {}), ({3, 7}, {}), ({4, 5}, {}), ({4, 6}, {}), ------------------------------------------------------------------------ ({5, 7}, {}), ({6, 7}, {})} o2 : List

To actually see the polyhedra of the complex we can look at their vertices, for example:
 i3 : vertPC = vertices PC o3 = | -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 o3 : Matrix QQ <-- QQ i4 : apply(L, l -> vertPC_(l#0)) o4 = {| -1 1 |, | -1 -1 |, | -1 -1 |, | 1 1 |, | 1 1 |, | -1 1 |, | -1 | -1 -1 | | -1 1 | | -1 -1 | | -1 1 | | -1 -1 | | 1 1 | | 1 | -1 -1 | | -1 -1 | | -1 1 | | -1 -1 | | -1 1 | | -1 -1 | | -1 ------------------------------------------------------------------------ -1 |, | 1 1 |, | -1 1 |, | -1 -1 |, | 1 1 |, | -1 1 |} 1 | | 1 1 | | -1 -1 | | -1 1 | | -1 1 | | 1 1 | 1 | | -1 1 | | 1 1 | | 1 1 | | 1 1 | | 1 1 | o4 : List

## Ways to use polyhedra :

• polyhedra(ZZ,PolyhedralComplex)

## For the programmer

The object polyhedra is .