Compound of two tetrahedra
In geometry, a compound of two tetrahedra is constructed by two overlapping tetrahedra, usually implied as regular 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.
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.
Other orientations can be chosen as 2 tetrahedra within the compound of five tetrahedra and compound of ten tetrahedra:
...
Wikipedia