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<sub>3d</sub>, 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.
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.