Cruciform

The Cruciform Composition uses all possible domes of the symmetry family which are included in the traditional central 32-fold dome. The central dome uses 15 of the 16 muqarnas tiles of 32-fold symmetry. The unused tile, 16, is in the vertical plane. (See image) Its use on the outside would prevent this as a possible composition. The four surrounding secondary domes use 7 of the 32-fold muqarnas tiles. The next smaller tertiary domes use 3 of the 32-fold muqarnas tiles. The final smallest quaternary domes use a single (90°) tile of the 32-fold muqarnas tiles. All similar tiles are colored identically to aid in understanding the dome sequence.

The 32-fold family contains the tiles of the 16-fold, the 8-fold, and the 4-fold families. Each larger denomination family includes the tiles of all smaller families. Thus if one were to create a 64-fold family it would contain 32 unique tiles, 16 of which would already be part of the 32-, 16-, 8-, and 4-fold families. The coloring of the various tile types is an aid to seeing the inclusion of previous symmetry family tiles.