Bourgoin, Plate 129

This pattern was surely incorrectly drawn by Bourgoin since the black hexagon should be more nearly regular. See Bourgoin, Plate 129 (corrected).

• 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 45°.
• There are 6 non-regular reflective tiles (including 2 kites) and one reflective pair.
• The tiling satisfies the interlace condition and has no finite interlace and two infinite interlaces with straight cross-overs.
• The tiling is edge-to-edge.
• As drawn, contains about 409 polygons.

1. Page 294 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 129 (No exact source known) 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 129

Photo?

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