111252X3 Seed Dome with Two Tiers

This dome is expanded with the Ray motif. The overall organization is three-fold, 3X(), or three-sided.

Specification
Animation
4K – 3840 X 2160
Symmetry Group [SG]
36-fold, 18 tiles
Symmetry of Form
3-fold
Form Group
Dome
Seed
(111252)X3*
Motif(s)
Ray
Motif(s) Angle(s)
Number of Tiers
2
SG – Tiles Used
1 – 5, 7 – 17
(NOT 6 or 18)
Edge Type
Straight

* On this page.

Explanation of the 111252X3 Seed

Detail of the 111252X3 SeedDetail of the 111252X3 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, 10º, 10º, 20º, 50º, 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 + 10 + 10 + 20 + 50 + 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.)

Plan View of Entire 36-Fold Dome with the 111252X3 Seed HighlightedPlan View of Entire 36-Fold Dome with the 111252X3 Seed Highlighted

111252X3 Seed Dome Expanded to Two Tiers with Ray Motif

Please see Ray Motif (here)

Plan Views of the 12 Unique Rays of the 111252X3 Seed

Plan Views of the 12 Unique Rays of the (111252)X3 Seed

The 12 Unique Rays of the 111252X3 Seed Determine Its Geometry

The 111252X3 tier expansion requires adding the mogharnas rays, thus providing a viable framework for completing the dome’s tiers. Twelve unique rays are created by this seed. The two green rays have the greatest symmetry and are mirror reflections of themselves. Also, they occur on the three axes of the domes three-fold symmetry. The other ten rays are made of five chiral pairs. That is, one of the pair is like the right hand to the left hand of the other. Of course, rays must be placed correctly, both vertically and horizontally to be successful.
 
By adding mogharnas surfaces/tiles to bridge the gaps between the twelve 111252X3 Rays, the first and second tiers of the dome are completed. This results in a series of tapeworm-like bands of edge-joined muqarnas tiles. These bands are most easily seen in the view of the left which shows all twelve rays of the 111252X3 seed simultaneously.

Sketch of 111252X3 Seed

Initial sketch of the 111252X3 Seed

Importantly, designing mogharnas domes with the Seed approach provides results in novel muqarnas designs. Finally, seed designs can easily be done “on the back of a napkin.” This is my sketch for the 111252X3 seed.