normalFan -- computes the normalFan of a polyhedron

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 = P

o1 : Polyhedron

i2 : F = normalFan P

o2 = F

o2 : Fan

i3 : raysF = rays F

o3 = | 1 -1 0 |
     | 0 -1 1 |

              2       3
o3 : Matrix ZZ  <-- ZZ

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

o4 = {| 1 0 |, | -1 0 |, | 1 -1 |}
      | 0 1 |  | -1 1 |  | 0 -1 |

o4 : List

Ways to use normalFan:

normalFan(Polyhedron)

For the programmer

The object normalFan is a method function.

The source of this document is in Polyhedra/documentation/old_documentation.m2:2740:0.