The best known is the compound of two tetrahedra called the stella octangula, discovered by Kepler. The vertices define a cube and the intersection of the two an octahedron, which shares the same faceplanes as the compound. Thus it is a stellation of the octahedron, and in fact, the only stellation thereof.
The stella octangula is one of only five compounds that are vertex, edge, and faceuniform, called regular compounds:
Components Vertices Faceplanes Symmetry group                       2 tetrahedra Cube Octahedron Oh 5 tetrahedra Dodecahedron Icosahedron I 10 tetrahedra Dodecahedron Icosahedron Ih 5 cubes Dodecahedron Rhombic triacontahedron[?] Ih 5 octahedra Icosidodecahedron Icosahedron Ih
The compound of 5 tetrahedra actually comes in two enantiomorphic versions, which together make up the compound of 10 tetrahedra. Each of the tetrahedral compounds is selfdual, and the compound of 5 cubes is dual to the compound of 5 octahedra.
The stella octangula can also be regarded as a compound of a tetrahedron with its dual polyhedron, inscribed in a common sphere so that the vertices of one line up with the face centres of the other. The corresponding cubeoctahedron and dodecahedronicosahedron compounds are the first stellations of the cuboctahedron and icosidodecahedron, respectively.
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