Wallpaper Patterns

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Wallpaper catalog of Remondini - Bassano - Italy, 18th century

Suggested reading:

  • Visions of Symmetry, pg. 31-44, 77-78.

Relevant examples from Escher's work:

  • Escher's sketches of Polya's 17 wallpaper patterns. Visions of Symmetry, pg. 24-26.

Wallpaper Patterns

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A wallpaper pattern is a plane figure which has more than one direction of translation symmetry. Most actual wallpaper fits the bill, because it must repeat left to right in order to hang in strips, and it must repeat vertically so that multiple strips can be cut from the same roll.

The lattice of translations.

The Seventeen Wallpaper Groups

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File:Test1.svg File:Test2.svg File:Test3.svg

Escher's Use of Symmetry

Escher's Regular Division of the Plane Drawings served as source material for his finished printed works. The vast majority of these fall into one of seven symmetry groups: p1, p2, p3, p4, p6, pg, and pgg. These are exactly the symmetry groups which have no reflection symmetry - only translation, rotation, and glide reflection. If two creatures meet on a line of mirror symmetry, they must have a flat edge, and recognizable figures from life rarely have perfectly straight edges. Because of this, Escher mostly avoided mirror symmetyr, although he did create a few drawings where bilateral symmetry of the motif leads to overall mirror symmetry of the pattern.


Wallpaper Exercises

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