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 (1) 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.

 

Sixteen (16) = 180.0°
Vertical & Planar
Tile Sixteen (16)
16 X 11.25°

The complete set of 16 tiles may be seen here.

Dome PrimacyMuqarnas Tiles UsedTile TotalAngles 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

Cruciform Composition, Perspective View
Cruciform Composition, Perspective View

Cruciform Composition Domes, Perspective View
Cruciform Composition Domes

Cruciform Composition Domes, Plan View
Cruciform Composition Domes, Plan View

8-fold Dome, Perspective View
8-fold Dome, Perspective View

8-fold Dome, Side View
8-fold Dome, Side View

8-fold Dome, Top View
8-fold Dome, Top View