# Compound of two tetrahedra

In geometry, a compound of two tetrahedra is constructed by two overlapping tetrahedra, usually implied as regular tetrahedra.

## Stellated octahedron

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.

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 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.

## Lower symmetry constructions

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

Examples
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

## Other compounds

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: