8-fold Muqarnas

The Four Unique Tiles of the 8-fold Symmetry Muqarnas

8-fold mogharnas tiles possess octagonal symmetry. They have apex angles of 45°, 90°, 135° & 180° in the plan view. The 180° tile is visible as a line in the plan view.

Comparison of 8-fold Symmetry Mogharnas Domes

The three dome plan views show how I attempted to make them all approximately the same area.

I interpreted the Ammann-Beenker A5 (AB-A5) Tiling as a plan view of a muqarnas dome with the dome peak in the image center. Animation

Plan View of Eight-fold Crescent Motif Dome Overlaid on AB-A5 Dome
Animation

Plan View of Eight-fold Ray Motif Onion Dome Overlaid on AB-A5 Dome
Animation

Impact of Design Approach Upon Verticality

Side Views of 8-fold Domes Show the Impact on Height of Vertical Faces & Onion Dome Technique

The pink dome side view is the AB-A5 dome. It only uses 3 of the 4 8-fold mogharnas tiles. The indigo color is the eight-fold crescent motif dome and uses vertical faces and so is steeper than AB-A5. The yellow eight-fold ray motif onion dome uses vertical faces and both inner and outer sloping onion faces, thus making it the highest and steepest of all. This difference is with Identical constituent elements (tiles). Of course, a steeper set of tiles results in taller and steeper results through different means.