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# directProduct(Cone,Cone) -- computes the direct product of polyhedra and cones

## Description

The directProduct of X and Y is the polyhedron {(x,y) | x in X, y in Y} in the direct product of the ambient spaces. If X and Y are both cones, then the direct product is again a cone and the output is then also given as a Cone, otherwise as a Polyhedron.
 i1 : P = hypercube 1 o1 = {ambient dimension => 1 } dimension of lineality space => 0 dimension of polyhedron => 1 number of facets => 2 number of rays => 0 number of vertices => 2 o1 : Polyhedron i2 : Q = hypercube 2 o2 = {ambient dimension => 2 } dimension of lineality space => 0 dimension of polyhedron => 2 number of facets => 4 number of rays => 0 number of vertices => 4 o2 : Polyhedron i3 : directProduct(P,Q) == hypercube 3 o3 = true

See also Cone * Cone, Cone * Polyhedron, Polyhedron * Cone, and Polyhedron * Polyhedron.

## Ways to use this method:

• directProduct(Cone,Cone) -- computes the direct product of polyhedra and cones
• "directProduct(Cone,Polyhedron)"
• "directProduct(Polyhedron,Cone)"
• "directProduct(Polyhedron,Polyhedron)"