Bourgoin, Plate 32

data203/B032A (Click on image for high-quality PDF version)

Version with regular 5-star: Bourgoin, Plate 32 and version with neither regular heptagon or regular 5-star: Bourgoin, Plate 32.

Geometry

The symmetry group of the tiling is *632 (p6m).
All the internal angles of the constituent polygons are a multiple of 2.14 (π/84)°.
Contains one regular heptagon.
Contains one regular 6-pointed star polygon with vertex angle of 77.14 (3π/7)°.
There are five non-regular reflective tiles.
The tiling satisfies the interlace condition and has two finite interlaces and one infinite interlace with straight cross-overs.
The tiling is edge-to-edge.
As drawn, contains about 195 polygons.

Publications referenced:

Fig 13.3a of Brian Wichmann and David Wade. Islamic Design: a Mathematical Approach, Springer, 2017. ISBN 978-3-319-69. [ww] {}
Photo by Goossen Karssenberg (Friday mosque, Isfahan, Iran) of Not specific. Personal Communication, Information sent to the author, 21c. [pc]
Plate 32 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.

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