| bgcolor=#e7dcc3 colspan=2 | Compound of four cubes | |
|---|---|---|
| align=center colspan=2 | (Animation) | |
| Type | Compound | |
| Convex hull | Chamfered cube | |
| Polyhedra | 4 cubes | |
| Faces | 32 squares | |
| Edges | 48 | |
| Vertices | 32 (8 + 24) | |
| Symmetry group | octahedral (Oh) | |
| Subgroup restricting to one constituent | 3-fold antiprismatic (D3d) |
Its Cartesian coordinates are (±3, ±3, ±3) and the permutations of (±5, ±1, ±1).
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The eight vertices on the 3-fold symmetry axes can be seen as the vertices of a fifth cube of the same size.[3] Referring to the images below, the four old cubes are called colored, and the new one black.Each colored cube has two opposite vertices on a 3-fold symmetry axis, which are shared with the black cube. (In the picture both 3-fold vertices of the green cube are visible.) The remaining six vertices of each colored cube correspond to the faces of the black cube. This compound shares these properties with the compound of five cubes (related to the dodecahedron), into which it can be transformed by rotating the colored cubes on their 3-fold axes.
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