# 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 = {ambient dimension => 3 } number of generating polyhedra => 1 top dimension of the polyhedra => 3 o1 : PolyhedralComplex i2 : L = polyhedra(2,PC) o2 = {{ambient dimension => 3 }, {ambient dimension => 3 dimension of lineality space => 0 dimension of lineality space => dimension of polyhedron => 2 dimension of polyhedron => 2 number of facets => 4 number of facets => 4 number of rays => 0 number of rays => 0 number of vertices => 4 number of vertices => 4 ------------------------------------------------------------------------ }, {ambient dimension => 3 }, {ambient dimension => 3 0 dimension of lineality space => 0 dimension of lineality space dimension of polyhedron => 2 dimension of polyhedron => 2 number of facets => 4 number of facets => 4 number of rays => 0 number of rays => 0 number of vertices => 4 number of vertices => 4 ------------------------------------------------------------------------ }, {ambient dimension => 3 }, => 0 dimension of lineality space => 0 dimension of polyhedron => 2 number of facets => 4 number of rays => 0 number of vertices => 4 ------------------------------------------------------------------------ {ambient dimension => 3 }} dimension of lineality space => 0 dimension of polyhedron => 2 number of facets => 4 number of rays => 0 number of vertices => 4 o2 : List

To actually see the polyhedra of the complex we can look at their vertices, for example:

 i3 : apply(L,vertices) 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 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 | o3 : List

## Ways to use polyhedra :

• "polyhedra(ZZ,PolyhedralComplex)"

## For the programmer

The object polyhedra is .