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OldPolyhedra :: incompPolyhedra

incompPolyhedra -- returns the pairs of incompatible polyhedra

Synopsis

Description

If incompPolyhedra is applied to a list of polyhedra and polyhedral complexes, then it returns the pairs of elements whose intersection is not a face of each. For a Polyhedron P and a PolyhedralComplex PC in the list this means there is at least one generating Polyhedron of PC whose intersection with P is not a face of each. For two polyhedral complexes in the list this means there is at least one generating polyhedron each such that their intersection is not a face of each. If applied to a pair consisting of a polyhedron and a polyhedral complex or two polyhedral complexes, then it returns the pairs of polyhedra that do not share a common face.

i1 : P1 = convexHull matrix {{1,0,0},{1,1,0}};
i2 : P2 = convexHull matrix {{1,0,0},{0,-1,0}};
i3 : P3 = convexHull matrix {{-1,0,0},{0,1,0}};
i4 : P4 = convexHull matrix {{1,1,0},{0,1,0}};
i5 : P5 = convexHull matrix {{1,2,0},{2,1,0}};
i6 : L = {P1,P2,P3,P4,P5};
i7 : Lpairs = incompPolyhedra L

o7 = {({ambient dimension => 2           }, {ambient dimension => 2         
        dimension of lineality space => 0    dimension of lineality space =>
        dimension of polyhedron => 2         dimension of polyhedron => 2   
        number of facets => 3                number of facets => 3          
        number of rays => 0                  number of rays => 0            
        number of vertices => 3              number of vertices => 3        
     ------------------------------------------------------------------------
      }), ({ambient dimension => 2           }, {ambient dimension => 2      
     0      dimension of lineality space => 0    dimension of lineality space
            dimension of polyhedron => 2         dimension of polyhedron => 2
            number of facets => 3                number of facets => 3
            number of rays => 0                  number of rays => 0
            number of vertices => 3              number of vertices => 3
     ------------------------------------------------------------------------
         })}
     => 0

o7 : List
i8 : Lpairs == {(P1,P4),(P1,P5)}

o8 = false

Ways to use incompPolyhedra :

For the programmer

The object incompPolyhedra is a method function.