Compound of twenty tetrahemihexahedra

This uniform polyhedron compound is a symmetric arrangement of 20 tetrahemihexahedra. It is chiral with icosahedral symmetry (I).

Compound of twenty tetrahemihexahedra
Type	Uniform compound
Index	UC19
Polyhedra	20 tetrahemihexahedra
Faces	20+60 triangles, 60 squares
Edges	240
Vertices	60
Symmetry group	chiral icosahedral (I)
Subgroup restricting to one constituent	3-fold rotational (C3)

John Skilling notes, in his enumeration of uniform compounds of uniform polyhedra, that this compound of 20 tetrahemihexahedra is unique in that it cannot be obtained by "adding symmetry to a group in which the basic polyhedron is uniform". Each tetrahemihexahedron in this compound is embedded with symmetry group C₃, which does not act transitively over the tetrahemihexahedron's six vertices. However, the compound as a whole can achieve uniformity because two tetrahemihexahedra coincide at each vertex.