# incompPolyhedra -- returns the pairs of incompatible polyhedra

## Synopsis

• Usage:
Lpairs = incompPolyhedra L
Lpairs = incompPolyhedra(X,PC)
Lpairs = incompPolyhedra(PC,X)
• Inputs:
• Outputs:

## 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 = {(P1, P5), (P4, P5)} o7 : List``` ```i8 : Lpairs == {(P1,P4),(P1,P5)} o8 = false```

## Ways to use incompPolyhedra :

• incompPolyhedra(List)
• incompPolyhedra(PolyhedralComplex,PolyhedralComplex)
• incompPolyhedra(PolyhedralComplex,Polyhedron)
• incompPolyhedra(Polyhedron,PolyhedralComplex)