Compound of five cubes  

Type  Regular compound 
Stellation core  rhombic triacontahedron 
Convex hull  Dodecahedron 
Index  UC_{9} 
Polyhedra  5 cubes 
Faces  30 squares 
Edges  60 
Vertices  20 
Dual  Compound of five octahedra 
Symmetry group  icosahedral (I_{h}) 
Subgroup restricting to one constituent  pyritohedral (T_{h}) 
This polyhedral compound is a symmetric arrangement of five cubes. This compound was first described by Edmund Hess in 1876.
It is one of five regular compounds, and dual to the compound of five octahedra.
It is one of the stellations of the rhombic triacontahedron. It has icosahedral symmetry (I_{h}).
Its convex hull is a regular dodecahedron. It additionally shares its edge arrangement with the small ditrigonal icosidodecahedron, the great ditrigonal icosidodecahedron, and the ditrigonal dodecadodecahedron.
Small ditrigonal icosidodecahedron 
Great ditrigonal icosidodecahedron 
Ditrigonal dodecadodecahedron 
Dodecahedron (convex hull) 
Compound of five cubes 
The compound of ten tetrahedra can be formed by taking each of these five cubes and replacing them with the two tetrahedra of the Stella octangula (which share the same vertex arrangement of a cube).
This compound can be formed as a stellation of the rhombic triacontahedron. The 30 rhombic faces exist in the planes of the 5 cubes.
The stellation facets for construction are:
