Three Motif Dome

From the top the motifs are: 3232322, 4445, 656

4K – 3840 X 2160
Symmetry Group [SG]
36-fold, 18 tiles
Symmetry of Form
Form Group
3232322*, 4445*, 656*
Motif(s) Angle(s)
Number of Tiers
SG – Tiles Used
All 18
Edge Type

* On this page.

What Are These Three Motifs?

Diagrams of the three motifs: 3232322, 4445, & 656Diagrams of the three motifs: 3232322, 4445, & 656 

This construction demonstrates conclusively how different motifs can be employed in the design of multi-tiered mogharnas constructions. Prior to this I had always used the same motif, Ray or Crescent, for example, on any additional tiers.

Detail of the 1272X3 SeedDetail of the 1272X3 Seed

As will be shown, the mogharnas seed determines and describes the 36-fold mogharnas tiles which make up its top row, which is its radial center. Furthermore, each seed integer represents the plan view angle of the top vertex of the corresponding muqarnas tile. In this case, (10º, 20º, 70º, 20º) X 3. The X 3 shows that the set in the () is repeated three times. Clearly, the total of the plan view angles of a seed equals 360º. That is, 360 = 3 (10 + 20 + 70 + 20). 
I always expand from the seed outward with the minimum number of mogharnas tiles. However, that isn’t necessary and is another line of possible inquiry. 
The Ray motif approach is used to expand the dome and add two tiers to it. Note: a single seed mogharnas tile, i.e. (1) X 36 has two unique Ray types. (Example here.)

Front and Side View of 1272X3 36-Fold DomeFront and Side View of 1272X3 36-Fold Dome