crossPolytope -- computes the d-dimensional crosspolytope with diameter 2s

Usage:

P = crossPolytope(d,s)
Inputs:
- d, an integer, strictly positive
- s, ZZ or QQ, positive (optional)
Outputs:
- P, a convex polyhedron

Description

The d-dimensional crossPolytope with diameter s is the convex hull of +/- s times the standard basis in QQ^d. If s is omitted it is set to 1.

i1 : P = crossPolytope(3,3/2)

o1 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of polyhedron => 3
      number of facets => 8
      number of rays => 0
      number of vertices => 6

o1 : Polyhedron

i2 : vertices P

o2 = | -3/2 3/2 0    0   0    0   |
     | 0    0   -3/2 3/2 0    0   |
     | 0    0   0    0   -3/2 3/2 |

              3       6
o2 : Matrix QQ  <-- QQ

Ways to use crossPolytope:

crossPolytope(ZZ)
crossPolytope(ZZ,QQ)
crossPolytope(ZZ,ZZ)

For the programmer

The object crossPolytope is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/OldPolyhedra.m2:7416:0.