fVector -- computes the f-vector of a Cone or Polyhedron

Synopsis

• Usage:

  f = fVector C

  f = fVector P

• Inputs:
  • C, a convex rational cone
  • P, a convex polyhedron
• Outputs:
  • L, a list, containing the number of faces for each codimension

Description

The i-th entry of the f-vector of P is the number of dimension i-1 faces of P, so it starts with the number vertices, has dim(P)+1 entries, and the last entry is 1 for P itself. It is the same for a Cone C.

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 : fVector P

o2 = {5, 9, 6, 1}

o2 : List