normalFan -- computes the normalFan of a polyhedron

Synopsis

• Usage:

  F = normalFan P

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

Description

The normalFan of a Polyhedron is the fan generated by the cones C_v for all vertices v of the Polyhedron, where C_v is the dual Cone of the positive Hull of P-v. If P is compact, i.e. a polytope, then the normalFan is complete.

i1 : P = convexHull matrix{{1,0,0},{0,1,0}}

o1 = {ambient dimension => 2           }
      dimension of lineality space => 0
      dimension of polyhedron => 2
      number of facets => 3
      number of rays => 0
      number of vertices => 3

o1 : Polyhedron

i2 : F = normalFan P

o2 = {ambient dimension => 2         }
      number of generating cones => 3
      number of rays => 3
      top dimension of the cones => 2

o2 : Fan

i3 : apply(maxCones F,rays)

o3 = {| 1 0 |, | -1 0 |, | 1 -1 |}
      | 0 1 |  | -1 1 |  | 0 -1 |

o3 : List