17 cubes are distributed symmetrically. They share a common center point. A primary, or original cube, shown in black, is copied to 4 positions. Then each copy is copied 3 times to new positions.

A 3D design created in vZome. Use your mouse or touch to interact.

Scenes shows some stages of this construction. The Cube plus 4 model shows copies generated by rotating the original cube about each of its corner-to-corner axes in turn by 60°. These 4 cubes, colored red, blue, yellow and green, are then copied by rotation in the same way to 3 new positions each, generating 12 cubes. This “third generation” of cubes are shown in lighter shades of the strong colors of the four.

*A note for vZome users; The rotation process described is in practice accomplished by mirror planes and symmetry tools.*

An interesting feature of the overall symmetry can be seen in the Convex Hull 17 Cubes model in Scenes. There are 3 square panels adjoining each 3-fold vertex, for a total of 24, which are all the same size as the 6 that are parallel with primary cube faces.