Painted wooden ceiling, Cairo

Compare with Bourgoin, Plate 179.

• The symmetry group of the tiling is 2*22 (cmm).
• All the internal angles of the constituent polygons are a multiple of 36°.
• Contains five regular two-pointed star polygons with vertex angle of 72°.
• Contains two regular pentagons.
• Contains one regular 10-pointed star polygon with vertex angle of 36°.
• There are five non-regular reflective tiles.
• The tiling satisfies the interlace condition and has two finite interlaces and no infinite interlace with straight cross-overs.
• The tiling is edge-to-edge.
• As drawn, contains about 393 polygons.

1. Page 177, Fig 6.25 (Abd al-Rahman Katkhuda, Cairo, Egypt. Painted wooden ceiling, water dispensary) of Eric Broug. Islamic Geometric Design, Thames and Hudson, 2013. ISBN 978050051695. [broug2] {Many excellent photos}(1744AD, 1157AH)
2. Fig 12.5b of Brian Wichmann and David Wade. Islamic Design: a Mathematical Approach, Springer, 2017. ISBN 978-3-319-69. [ww] {}

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