# vertices -- displays the vertices of a Polyhedron or a PolyhedralComplex

## Synopsis

• Usage:
V = vertices P
• Inputs:
• Outputs:
• V,

## Description

vertices returns the vertices of the Polyhedron or PolyhedralComplex P as the columns of the Matrix V.

 i1 : P = intersection(matrix{{1,-1},{0,-1},{-1,-1},{0,1}}, matrix{{0},{-1},{0},{1}}) o1 = {ambient dimension => 2 } dimension of lineality space => 0 dimension of polyhedron => 1 number of facets => 2 number of rays => 0 number of vertices => 2 o1 : Polyhedron i2 : vertices P o2 = | -1 1 | | 1 1 | 2 2 o2 : Matrix QQ <--- QQ i3 : PC = skeleton(2,polyhedralComplex hypercube 3) o3 = {ambient dimension => 3 } number of generating polyhedra => 6 top dimension of the polyhedra => 2 o3 : PolyhedralComplex i4 : vertices PC 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 | 3 8 o4 : Matrix QQ <--- QQ

## Ways to use vertices :

• "vertices(PolyhedralComplex)"
• "vertices(Polyhedron)"

## For the programmer

The object vertices is .