Bourgoin, Plate 58

Extremely common, especially in western Islam, giving rise to many variants

• The symmetry group of the tiling is *442 (p4m).
• All the internal angles of the constituent polygons are a multiple of 45°.
• Contains three regular 8-pointed star polygons with vertex angle of 90°.
• There are 6 non-regular reflective tiles (including one kite and one dart).
• The tiling satisfies the interlace condition and has no finite interlace and one infinite interlace with straight cross-overs.
• The tiling is edge-to-edge.
• As drawn, contains about 307 polygons.

1. Photo by David Wade: MOR 0316 (Attarine Madrasah, Fez, Morocco) from [wadei] (1325AD, 725AH)
2. Page 76, Fig 3.34 (Alcazar, Seville, Spain. Wooden door) from [broug2] (1616AD, 1025AH)
3. Fig 9.6a from [ww]
4. Page 22 (Great Mosque, Damascus, Syria. Marble inlay) from [dury]
5. Page 239 from [abas]
6. Photo by David Wade: SPA 2315/2109x (Alcazar, Seville, Spain) from [wadei]
7. Plate 58 from [bourgoin]
8. Vol 1, page 410 (Royal Palace, Fez, Morocco) from [paccard]

• Wade photo BOU 058
• Wade photo MOR 0316
• Wade photo SPA 2315
• Wade photo SPA 2109x

• Tiling whose tile angles are a multiple of 45° and whose lengths are p+q*sqrt(2).

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