Complex

Complex Mogharnas Composition

Composed of Six Muqarnas Forms

This mogharnas composition contains six distinct forms joined seamlessly. It uses only muqarnas tiles – 15 of the 16 unique tiles or surfaces of the 32-fold symmetry muqarnas family.
The six distinct forms are:

1.) Traditional dome – twice (All other forms are used only once.)
2.) Flattened dome
3.) Small flattened enclosing form around traditional and flattened domes
4.) First tier Ray expansion of central dome
5.) Second tier Scarab and Vulture expansion of Ray first tier
6.) Large flattened enclosing form around everything

Note: The flattened enclosing forms (large and small) display mirror symmetry. The other forms display rotational symmetry, 32-fold or 2-fold.

Overall View

This is a striking example of compositions of muqarnas. I present a simple analysis of the most complex muqarnas which I have created. This exterior view of it from above shows its complexity. As you can see it is composed of multiple different forms. Yet it uses only the 16 unique muqarnas tiles without any gaps. Its 16 tiles are based upon the regular 32-gon. As a result, it is a single surface without holes or overlaps. No half tiles or irregular gap filling tiles used. The power of muqarnas as a flexible space-enclosing system is revealed. Drawing showing relationships of composition elements.

Basic Dome

This traditional muqarnas dome is the most basic form in this composition. It can be seen in two places. Most importantly, it is the source of all other muqarnas forms.

Chrysanthemum Dome

The ‘chrysanthemum’ flat dome is the next element. It’s hard to see in the overall composition. So I include its animation and the animation of it combined with the traditional dome and the unique forms which fill in between them.

Larger Dome
The larger dome contains a traditional dome on top with two other layers. Each layer has a different style or motif. Immediately below the traditional dome is a ‘Ray’ expansion tier. Below it is a more exotic second tier. I discovered it accidentally. It has two planes of symmetry at right angles.

Plan View of the Entire Composition
This view shows the large, unfinished enclosing circle. Its two halves mirror each other. The adjacent forms’ edges determine their shape. Like many mogharnas shapes, there is an inevitability to them. This is a result of the strict geometric definition of the muqarnas tiles themselves.