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Compound of two truncated tetrahedra

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Compound of two truncated tetrahedra
Type Uniform compound
Index UC54
Schläfli symbol a2{4,3}
Coxeter diagram + =
Polyhedra 2 truncated tetrahedra
Faces 8 triangles
8 hexagons
Edges 36
Vertices 24
Symmetry group octahedral (Oh)
Subgroup restricting
to one constituent
tetrahedral (Td)

This uniform polyhedron compound is a composition of two truncated tetrahedra, formed by truncating each of the tetrahedra in the stellated octahedron. It is related to the cantic cube construction of the truncated tetrahedron, as , which is one of the two dual positions represented in this compound.

The vertex arrangement is the same as a convex, but nonuniform rhombicuboctahedron having 12 rectangular faces.


  • Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (3): 447–457, doi:10.1017/S0305004100052440, MR 0397554.