Bourgoin, Plate 151

• The symmetry group of the tiling is *442 (p4m).
• All the internal angles of the constituent polygons are a multiple of 22.5°.
• Contains two regular octagons.
• Contains one regular four-pointed star polygon with vertex angle of 45°.
• Contains one regular 8-pointed star polygon with vertex angle of 90°.
• There are three 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 209 polygons.

1. Page 322 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 151 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.
3. See analysis of interlacing of B Grünbaum and G C Shephard. Interlace Patterns in Islamic and Moorish Art, Leonardo, Vol. 25, No. 3/4, pp. 331-339, 1992. [gands2] Copyright controlled copy on Internet.

• Wade photo BOU 151

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