Bourgoin, Plate 32
data158/B032
(Click on image for high-quality PDF version)
Version with regular heptagon: 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 12°.
- Contains one regular five-pointed star polygon with vertex angle of 48°.
- Contains one regular 6-pointed star polygon with vertex angle of 84°.
- 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 222 polygons.
References
Publications referenced:
- Plate 43 (Nur al-Din Bimaristan, Damascus, Syria. Main door) of E Herzfeld. Damascus: Studies in Architecture: I, Ars Islamica Vol9, pp1-53, 1942. [herzfeld2] {} Copyright controlled copy on Internet.(1152AD, 546AH)
- Fig 13.3b of Brian Wichmann and David Wade. Islamic Design: a Mathematical Approach, Springer, 2017. ISBN 978-3-319-69. [ww] {}
- Plate 32 (Inexact heptagon, uncertain source) 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.
Photographs
v47