Composition of 53 domes

Composition of 53 domes

This arrangement of muqarnas domes is in a cruciform pattern. At the center is a traditional, simple dome. It is made up of thirty-two of each of the fifteen types of muqarnas tiles. Thus, it has a total of 32 X 15 = 480 muqarnas tiles.

Surrounding it are four domes made up of sixteen of seven tiles (2, 4, 6, 8, 10, 12, 14), each dome with a total of 16 X 7 = 112 muqarnas tiles.

Each of these four domes is in turn surrounded by three smaller domes (not four, because of their adjacency to the large central dome). These domes are made of eight of each of three muqarnas tiles (4, 8, 12) for a total of 8 X 3 = 24 muqarnas tiles per dome.

Finally, each of these smaller domes is surrounded by three domes that are made up of four tiles each that are all the same type (8). Naturally muqarnas tile 8 has 90 angles in the plan view.

The total number of domes = 1 + 4 + (3 X 4) + (3 X 3 X 4) = 1 + 4 + 12 + 36 = 53.

The total number of tiles = 480 + (4 X 112) + (3 X 4 X 24) + (3 X 3 X 4 X 4) =
                            480 + 448 + 288 + 144 = 1360 tiles

This is the interesting relationship between the domes and their tiles.
(The numbers are the tile numbers.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  Full dome
  2   4   6   8   10    12    14     Secondary dome
      4       8         12           Tertiary dome
              8                      Minimal dome

An animation of this arrangement of muqarnas domes can be seen on my YouTube channel HERE.