cyclicPolytope -- computes the d dimensional cyclic polytope with n vertices

Synopsis

• Usage:

  P = cyclicPolytope(d,n)

• Inputs:
  • d, an integer, strictly positive
  • n, an integer, strictly positive
• Outputs:
  • P, a convex polyhedron

Description

The d-dimensional cyclicPolytope with n vertices is the convex hull of n points on the moment curve in QQ^d. The moment curve is defined by t -> (t,t^2,...,t^d) and the function takes the points {0,...,n-1}.

i1 : P = cyclicPolytope(3,5)

o1 = {ambient dimension => 3           }
      dimension of lineality space => 0
      dimension of polyhedron => 3
      number of facets => 6
      number of rays => 0
      number of vertices => 5

o1 : Polyhedron

i2 : vertices P

o2 = | 0 1 2 3  4  |
     | 0 1 4 9  16 |
     | 0 1 8 27 64 |

              3        5
o2 : Matrix QQ  <--- QQ