Alhambra, Vestibule ceiling

• The symmetry group of the tiling is *442 (p4m).
• All the internal angles of the constituent polygons are a multiple of 22.5°.
• Contains one regular 8-pointed star polygon with vertex angle of 90°.
• Contains one regular 16-pointed star polygon with vertex angle of 67.5°.
• There are 9 non-regular reflective tiles (including 3 kites).
• The tiling satisfies the interlace condition and has one finite interlace and three infinite interlaces with straight cross-overs.
• The tiling is edge-to-edge.
• As drawn, contains about 931 polygons.

1. Photo by Nick Crossling (Alhambra, Mexuar patio, Spain. Vestibule ceiling) of Not specific. Personal Communication, Information sent to the author, 21c. [pc] (1232-1417AD, 629-820AH)
2. Fig 8.5, photo of Brian Wichmann and David Wade. Islamic Design: a Mathematical Approach, Springer, 2017. ISBN 978-3-319-69. [ww] {}

• Escher's Alhambra tiling pattern
• Stars with 16 points with vertex angle not equal to 45°

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