 | It has been suggested that this article be merged into Stellated octahedron . (Discuss) Proposed since March 2025. |
In geometry, a compound of two tetrahedra is a polyhedral compound 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.
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.
A tetrahedron and its dual tetrahedron |
Orthographic projections from the different symmetry axes | If the edge crossings were vertices, the mapping on a sphere would be the same as that of a rhombic dodecahedron. |
There are lower symmetry variations on this compound, based on lower symmetry forms of the tetrahedron.
| D4h, [4,2], order 16 | C4v, [4], order 8 | D3d, [2+,6], order 12 |
|---|---|---|
 Compound of two tetragonal disphenoids in square prism ß{2,4} or     |  Compound of two digonal disphenoids |  Compound of two right triangular pyramids in triangular trapezohedron |
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 the latter of which can be seen as a hexagrammic pyramid:
