This Chrysanthemum ceiling has the same number and type of mogharnas tiles as in a traditional muqarnas dome. However, they are arranged in a different manner which results in a much flatter “dome”.
Chrysanthemum Ceiling: 1-15-1-15 X8 Seed & Expansion
The 1-15-1-15 X8 Seed of this Chrysanthemum ceiling displays 8-fold symmetry. As a result when it is expanded with the Ray Motif it has a total of 8 distinct rays, in contrast to the Traditional Dome which only has 2 rays as shown here. Only 4 of the 8 Rays are shown here. All are shown below.
Chrysanthemum Ceiling, 1-15-1-15 X8 Seed, Top & Bottom Views
I include four views, 2 top and 2 bottom, of the Chrysanthemum ceiling. This is because it has an unusual shape along with the other seeds of flattened domes. This 1-15-1-15 X8 seed is similar to the mathematical form known as the “Octopus Saddle”. (See Below) The mathematical saddle shapes are a way of representing hyperbolic space in which, unlike Euclidean geometry, parallel lines diverge rather than staying equidistant. Saddle shapes which give rise to ever deeper valleys and higher ridges as one moves away from the central saddle. Flattened mogharnas / muqarnas domes develop out from the center in ‘waves’ of fixed height per type. The additional tiers of flattened domes are in integral multiples of the central flattened dome’s height.