Tiling 4.6.12

• The symmetry group of the tiling is *632 (p6m).
• All the internal angles of the constituent polygons are a multiple of 30°.
• Contains one square.
• Contains one regular hexagon.
• Contains one regular 12-gon.
• The tiling does not satisfy the two-colour condition.
• The tiling is edge-to-edge.
• As drawn, contains about 48 polygons.

1. Page 145 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 37, Figure 71 (Shibam-Kawkabin, Yemen) of I El-Said and A Parman. Geometric concepts in Islamic Art, World of Islam Festival Publishing Co, 1976. ISBN 090503503. [elsaid] {Gives sources of several interesting patterns.}
3. Tiling 4.6.12 (Known to the Greeks!) of Joseph S. Myers. Tiling with Regular Star Polygons, Eureka 56 (March 2004), 20-27, 2004. [myers] Available on Internet.

• Regular polygons with more than eight sides

Photo?

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