Compound of six tetrahedra

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Compound of six tetrahedra
UC03-6 tetrahedra.png
Type Uniform compound
Convex hull Nonuniform truncated octahedron
Index UC3
Polyhedra 6 tetrahedra
Faces 24 triangles
Edges 36
Vertices 24
Symmetry group octahedral (Oh)
Subgroup restricting to one constituent 2-fold antiprismatic (D2d)

This uniform polyhedron compound is a symmetric arrangement of 6 tetrahedra. It can be constructed by inscribing a stella octangula within each cube in the compound of three cubes, or by stellating each octahedron in the compound of three octahedra.


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