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.
The complete set of 16 tiles may be seen here.
Dome Primacy | Muqarnas Tiles Used | Tile Total | Angles Unique to N-fold |
---|---|---|---|
Primary Dome 32-fold | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, (16) | 15 (16) | 11.25° Increment 11.25, 33.75, 56.25, 78.75, 101.25, 123.75, 146.25, 167.75 |
Secondary Domes 16-fold | 2, 4, 6, 8, 10, 12, 14, (16) | 7 (8) | 22.5° Increment 22.5, 67.5, 112.5, 157.5 |
Tertiary Domes 8-fold | 4, 8, 12, (16) | 3 (4) | 45° Increment 45, 135 |
Quaternary Domes 4-fold | 8, (16) | 1 (2) | 90° Increment 90, 180 |
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