Samarra

• 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 8-pointed star polygon with vertex angle of 90°.
• There is one non-regular reflective tile.
• The tiling satisfies the interlace condition and has no finite interlace and one infinite interlace with straight cross-overs.
• The tiling is edge-to-edge.
• As drawn, contains about 55 polygons.

1. Figure 234, house 3, room 16 from [herzfeld1] (800-900AD, 183-286AH)
2. Burrell Collection, 33.55 (Shrine of Imamzada, Varamin, Iran) from [pc] (1261-2AD, 659-60AH)
3. British Museum G.466 (Iran) from [pc] (1262AD, 660AH)
4. Internet photo, LACMA (Iran. Star and cross tiles, probably Takht-i Sulaiman (AC1996.115.1-.5)) from [pc] (1270-80AD, 668-78AH)
5. (Fatehpur Sikri, Rajah Birbal's House, India) from [smith2] (1571AD, 978AH)
6. Figure 9 (Samarra, Iraq) from [lee]
7. I.10.6, bottom right, page 7 from [gands]
8. Internet photo 243 (house bait al-shalabi ceilings 18thc) from [d-avennes]
9. Metropolitan Museum of Art, 40.170.443 (Nishapur, Iran. Stucco; carved, with some cast plaster elements) from [pc]
10. Page 41 (Cappella Palatina, Italy) from [broug]
11. Pages 13 and 19 from [cahier]
12. Plate 27 from [wilson]
13. Plates 2-4 and Figure 15 from [elsaid]
14. XLIII(4) from [jones]

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

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