Bourgoin, Plate 44

• The symmetry group of the tiling is *442 (p4m).
• All the internal angles of the constituent polygons are a multiple of 45°.
• Contains one regular octagon.
• Contains one regular 8-pointed star polygon with vertex angle of 45°.
• There are two non-regular reflective tiles (including one kite).
• The tiling satisfies the interlace condition and has one finite interlace and no infinite interlace with straight cross-overs.
• The tiling is edge-to-edge.
• As drawn, contains about 175 polygons.

1. Page 236 of S J Abas and A S Salman. Symmetries of Islamic Geometrical Patterns, World Scientific, 1995. ISBN 981021704. [abas] {Very many patterns in black and white, no sources given.}
2. Plate 44 of J Bourgoin. Arabic Geometrical Pattern and Design, Dover, 1879. ISBN 048622924. [bourgoin] {Classical book of around 200 hand-produced patterns, in back and white.} Fuller version available on Internet.

• Wade photo BOU 044

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

Photo?

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