isReflexive -- checks if a Polytope is reflexive

Synopsis

• Usage:

  b = isReflexive P

• Inputs:
  • P, a convex polyhedron
• Outputs:
  • b, true if the Polyhedron is reflexive, false otherwise

Description

A lattice polytope P in the QQ space of a lattice $M$ is reflexive if its polar polytope is also a lattice polytope. The function checks if P is compact, a lattice polytope and if the dual is a lattice polytope.

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

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 : isReflexive P

o2 = true

See also

• isCompact -- checks compactness of a Polyhedron
• isLatticePolytope -- checks if a polyhedron is a lattice polytope
• polar -- computes the polar of a polyhedron