intersectFaces -- The intersection of two faces.

i1 : R=QQ[x_0..x_4];

i2 : C=simplex R

o2 = 4: x x x x x  
         0 1 2 3 4

o2 : complex of dim 4 embedded in dim 4 (printing facets)
     equidimensional, simplicial, F-vector {1, 5, 10, 10, 5, 1}, Euler = 0

i3 : F=C.fc_2_0

o3 = x x x
      0 1 2

o3 : face with 3 vertices

i4 : G=C.fc_2_1

o4 = x x x
      0 1 3

o4 : face with 3 vertices

i5 : intersectFaces(F,G)

o5 = x x
      0 1

o5 : face with 2 vertices

i6 : H=C.fc_2_2

o6 = x x x
      0 2 3

o6 : face with 3 vertices

i7 : intersectFaces({F,G,H})

o7 = x
      0

o7 : face with 1 vertex