Alhambra, Sala de las dos Hermanas

Taken from the end section of the ceiling in a side chamber of the Sala de las Dos Hermanas.

• The symmetry group of the tiling is *442 (p4m).
• All the internal angles of the constituent polygons are a multiple of 45°.
• Contains one regular four-pointed star polygon with vertex angle of 45°.
• Contains one regular 8-pointed star polygon with vertex angle of 90°.
• Contains one regular 8-pointed star polygon with vertex angle of 45°.
• There are five non-regular reflective tiles (including one kite and one dart).
• 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 407 polygons.

1. Photo from Nick Crossling (Alhambra, Sala de las Dos Hermanas, Spain. Wood inlay from a side gallery) of Not specific. Personal Communication, Information sent to the author, 21c. [pc]

• Tiling whose tile angles are a multiple of 45° and whose lengths are p+q*sqrt(2).

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