Cubic tegum

The cubic bipyramid is a convex isochoric polychoron with 12 square pyramids as cells. This polychoron can be made CRF.

Vertex coordinates
Coordinates for the vertices of a cubic bipyramid of edge length 1 are given by all permutations and changes of sign of the first three coordinates, and all sign changes of the last coordinate of:
 * (1/2, 1/2, 1/2, 0),
 * (0, 0, 0, 1/2)