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Polyhedra :: normalCone(Polyhedron,Polyhedron)

normalCone(Polyhedron,Polyhedron) -- computes the normal cone of a face of a polyhedron

Synopsis

Description

The normal cone of a face Q of a polyhedron P is the cone in the normal fan (see normalFan) that corresponds to this face. This is the cone of all vectors attaining their maximum on this face.

i1 : P = hypercube 3

o1 = P

o1 : Polyhedron
i2 : Q = convexHull matrix {{1,1,-1,-1},{1,-1,1,-1},{1,1,1,1}}

o2 = Q

o2 : Polyhedron
i3 : C = normalCone(P,Q)

o3 = C

o3 : Cone
i4 : rays C

o4 = | 0  |
     | 0  |
     | -1 |

              3        1
o4 : Matrix ZZ  <--- ZZ