commonFace checks if the intersection of C1 and C2 or the intersection of P1 and P2 is a face of both. If it is applied to a pair of a cone C and a fan F then it checks if the intersection of C with every generating cone of F is a face of each. For two fans it checks this condition for every pair of generating cones. If applied to a list then the list must contain Fans and Cones and it checks pairwise for a common face.
For example, consider the following three cones:
i1 : C1 = coneFromVData matrix {{1,0},{0,1}}; |
i2 : C2 = coneFromVData matrix {{1,-1},{0,-1}}; |
i3 : C3 = coneFromVData matrix {{1,-1},{2,-1}}; |
for each pair of two of them we can check if their intersection is a common face:
i4 : commonFace(C1,C2) o4 = true |
i5 : commonFace(C2,C3) o5 = true |
i6 : commonFace(C3,C1) o6 = false |