Roman mosaic, Pompei

• The symmetry group of the tiling is *2222 (pmm).
• All the internal angles of the constituent polygons are a multiple of 45°.
• Contains two squares.
• There is one non-regular reflective tile.
• The tiling satisfies the interlace condition and has no finite interlace and two infinite interlaces with straight cross-overs.
• The tiling is edge-to-edge.
• As drawn, contains about 161 polygons.

1. PP Class 27, [pmm,d2,d1], IH Class 65 of S J Dawes and B A Wichmann. A New Class of Tilings with Two Prototiles, Visual Mathematics, Vol 3, No 4., 2001. [dawes] {Revises CD/booklet.} Available on Internet.
2. Page 6 (top left) of Charles Cahier and Arthur Martin. 376 Decorative Allover Patterns from Historic Tilework and Textiles, Dover, 1868. ISBN 048626146. [cahier]
3. Pl 118 (d) (Pompei) of Catherine Balmelle .... Le décor géométrique de la mosaïque romaine, Paris, Picard, 2002. ISBN 270840624. [balmelle] {2 vols}

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

Photo?

v54