Compound of two tetrahedra

There is only one uniform polyhedral compound, the stellated octahedron, which has octahedral symmetry, order 48.

It has a regular octahedron core, and shares the same 8 vertices with the cube.

If the edge crossings were treated as their own vertices, the compound would have identical surface topology to the rhombic dodecahedron; were face crossings also considered edges of their own the shape would effectively become a nonconvex triakis octahedron.

There are lower symmetry variations on this compound, based on lower symmetry forms of the tetrahedron.

If two regular tetrahedra are given the same orientation on the 3-fold axis, a different compound is made, with D3h, [3,2] symmetry, order 12.