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
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}};
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i2 : P2 = convexHull matrix {{1,0,0},{0,-1,0}};
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i3 : P3 = convexHull matrix {{-1,0,0},{0,1,0}};
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i4 : P4 = convexHull matrix {{1,1,0},{0,1,0}};
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i5 : P5 = convexHull matrix {{1,2,0},{2,1,0}};
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i6 : L = {P1,P2,P3,P4,P5};
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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
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i8 : Lpairs == {(P1,P4),(P1,P5)}
o8 = false
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