Compound of three tetrahedra explained

bgcolor=#e7dcc3 colspan=2	Compound of 3 digonal antiprisms
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Type	Uniform compound
Uniform index	UC23 (n=3, p=2, q=1)
Polyhedra	3 digonal antiprisms (tetrahedra)
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, D_3d, 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

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.

References

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