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

Synopsis

• 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