Figure 2.0.1, Tiling by Kepler

• The tiling has no symmetry group and hence is not a repeat pattern.
• All the internal angles of the constituent polygons are a multiple of 36°.
• Contains 16 regular pentagons.
• Contains five regular decagons.
• Contains 9 regular five-pointed star polygons with vertex angle of 36°.
• There is one non-regular reflective tile.
• The tiling is edge-to-edge.
• As drawn, contains about 719 polygons.

• Page 57 of B Grünbaum and G C Shephard. Tilings and Patterns, W H Freeman, 1987. ISBN 071671193. [gands] {Most important work in this area.}

• Regular polygons with more than eight sides

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