This 5-dimensional 0/1-bipyramid has a twin, EQU5-7b.poly, which is combinatorially equivalent to it (also a 5-dimensional bipyramid over a 4-simplex), but which is not affinely equivalent: I this bipyramid the main diagonal is divided in the ratio 1:4, for the other one the ratio is 2:3.
DIM 5 VERTICES 1 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0 0 1 1 1 1 1 1 1 FACETS 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 3 -1 -1 -1 -1 1 -1 3 -1 -1 -1 1 -1 -1 3 -1 -1 1 -1 -1 -1 3 -1 1 -1 -1 -1 -1 3 AFFINE_HULL N_FACETS 10 AMBIENT_DIM 5 _version 1.5.1 _application polytope