Tiling on figure 2.1.5 (3.6.3.6) on page 63

This pattern is not quite what it seems. Each line is divided into two so the triangle is actually a star hexagon with a vertex angle of 60 degrees.

• The symmetry group of the tiling is *632 (p6m).
• All the internal angles of the constituent polygons are a multiple of 60°.
• Contains one regular three-pointed star polygon with vertex angle of 60°.
• Contains one regular 6-pointed star polygon with vertex angle of 120°.
• The tiling satisfies the interlace condition and has no finite interlace and one infinite interlace with straight cross-overs.
• The tiling is not edge-to-edge.
• As drawn, contains about 35 polygons.

1. Figure 1 (h) of Joseph S. Myers. Tiling with Regular Star Polygons, Eureka 56 (March 2004), 20-27, 2004. [myers] Available on Internet.
2. Figure 2.1.5, page 63 of B Grünbaum and G C Shephard. Tilings and Patterns, W H Freeman, 1987. ISBN 071671193. [gands] {Most important work in this area.}

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