Description
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 = posHull matrix {{1,0},{0,1}};

i2 : C2 = posHull matrix {{1,1},{0,1}};

i3 : C3 = posHull 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
