Wallpaper group
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A wallpaper group is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art, e
Example A: Cloth, Tahiti
Example B: Ornamental painting, Nineveh, Assyria
Example C: Painted porcelain, China
Medieval wall diapering
Tessellation
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A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellation can be generalized to
Wallpaper group
…The group p3 has three different rotation centres of order three (120°), but no reflections or glide reflections. Imagine a tessellation of the plane with equilateral triangles of equal size, with the sides corresponding to the smallest translations. Then half of the triangles are in one…
Zellige terracotta tiles in Marrakesh, forming edge‑to‑edge, regular and other tessellations
A wall sculpture in Leeuwarden celebrating the artistic tessellations of M. C. Escher
A temple mosaic from the ancient Sumerian city of Uruk IV (3400–3100 BC), showing a tessellation pattern in coloured tiles
Roman rhombille mosaic