Compound of two truncated tetrahedra

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Compound of two truncated tetrahedra
UC54-2 truncated tetrahedra.png
Type Uniform compound
Index UC54
Schläfli symbol a2{4,3}
Coxeter diagram CDel nodes 10ru.pngCDel split2.pngCDel node 1.png + CDel nodes 01rd.pngCDel split2.pngCDel node 1.png = CDel node h3.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.png
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 CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.png, 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.