Painted Mamluk ceiling

• The symmetry group of the tiling is *442 (p4m).
• All the internal angles of the constituent polygons are a multiple of 7.5°.
• Contains two regular two-pointed star polygons with vertex angle of 60°.
• Contains one regular octagon.
• Contains one regular 8-pointed star polygon with vertex angle of 90°.
• There are 7 non-regular reflective tiles (including one kite).
• The tiling satisfies the interlace condition and has three finite interlaces and no infinite interlace with straight cross-overs.
• The tiling is edge-to-edge.
• As drawn, contains about 249 polygons.

1. Page 289, Fig 176b (al-Mu'ayyad, Cairo, Egypt. Painted Mamluk ceiling) of Jay Bonner. Islamic Geometric Patterns, Springer, 2016. ISBN 978144190216. [bonner] {Largest Islamic tile collection in print}(1415-22AD, 817-25AH)

v54