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.

Distribution of 17 cubes

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.