Variant of Bourgoin Plate 167

This variant does not have an exact 7-pt star, unlike Bourgoin Plate 167.

• The symmetry group of the tiling is *2222 (pmm).
• Contains two regular heptagons.
• Contains one regular 14-pointed star polygon with vertex angle of 51.42 (2π/7)°.
• There are 8 non-regular reflective tiles (including one kite) and one reflective pair.
• The tiling satisfies the interlace condition and has no finite interlace and four infinite interlaces with straight cross-overs.
• The tiling is edge-to-edge.
• As drawn, contains about 629 polygons.

1. Plate 25 of Jules Bourgoin. Les arts arabes, Morel, Paris, 1873. [bour0] {Earlier work of Bourgoin} Available on Internet.
2. photo by Ayman Soliman (Abd al-Ghani al-Fakhri mosque, Cairo, Egypt. Minbar) of Not specific. Personal Communication, Information sent to the author, 21c. [pc]

• Tilings not constructible by straightedge and compass

v54