Bourgoin, Plate 144

• 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 octagons.
• Contains two regular 8-pointed star polygons with vertex angle of 90°.
• There are three non-regular reflective tiles.
• The tiling satisfies the interlace condition and has two finite interlaces and two infinite interlaces with straight cross-overs.
• The tiling is edge-to-edge.
• As drawn, contains about 331 polygons.

1. Page 187 of Keith Critchlow. Islamic Patterns - An Analytical and Cosmological Approach, Thames and Hudson, 1976. ISBN 050027071. [critchlow] {Gives about 6 patterns not found in Bourgoin.}
2. Page 250 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.}
3. Plate 144 (Uses the same tiles as Plate 52) 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 144

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

Photo?

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