faceFan -- computes the fan generated by the cones over the faces

Synopsis

• Usage:

  F = faceFan P

• Inputs:
  • P, a convex polyhedron
• Outputs:
  • F, an instance of the type Fan

Description

For a polyhedron with the origin in its relative interior, the face fan is the fan generated by the cones over the faces of the polytope. Hence the origin must be in the relative interior.

i1 : P = hypercube 2

o1 = P

o1 : Polyhedron

i2 : F = faceFan P

o2 = F

o2 : Fan

i3 : raysF = rays F

o3 = | -1 1  -1 1 |
     | -1 -1 1  1 |

              2        4
o3 : Matrix ZZ  <--- ZZ

i4 : apply(maxCones F, mc -> raysF_mc)

o4 = {| -1 -1 |, | 1  1 |, | -1 1  |, | -1 1 |}
      | -1 1  |  | -1 1 |  | -1 -1 |  | 1  1 |

o4 : List