Compound of three tetrahedra

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Compound of 3 digonal antiprisms
Compound of three tetrahedra.png
Type Uniform
Uniform index UC23 (n=3, p=2, q=1)
Polyhedra 3 digonal antiprisms
Faces 12 triangles
Edges 24
Vertices 12
Symmetry group D6d, order 12
Subgroup restricting
to one constituent
D2d, order 4

In geometry, a compound of three tetrahedra can be constructed by three tetrahedra rotated by 60 degree turns along an axis of the middle of an edge. It has dihedral symmetry, D3d, order 12. It is a uniform prismatic compound of antiprisms, UC23.

It is similar to the compound of two tetrahedra with 90 degree turns. It has the same vertex arrangement as the convex hexagonal antiprism.

Related polytopes[edit]

A subset of edges of this compound polyhedron can generate a compound regular skew polygon, with 3 skew squares. Each tetrahedron contains one skew square. This regular compound polygon containing the same symmetry as the uniform polyhedral compound.

Skew tetragons in compound of three digonal antiprisms.png


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

External links[edit]