nLab wallpaper group




A wallpaper group is a crystallographic group (space group) in dimension 2, hence a subgroup GIso( 2)G \subset Iso(\mathbb{R}^2) of the isometry group of the Euclidean plane such that

  1. the part of GG inside the translation group is generated by two linearly independent vectors;

  2. the point group is finite.

Fig. 3.10 in Tilley 2020:


e. g.

  • Richard Tilley, Sec. 3.5 in: Crystals and Crystal Structure, Wiley (2020) [ISBN:978-1-119-54838-6]

  • Patrick Morandi, The Classification of Wallpaper Patterns: From Group Cohomology to Escherís Tessellations (pdf)

See also

Discussion of meromorphic functions on the complex plane invariant under wallpaper groups:

  • Richard Chapling, Invariant Meromorphic Functions on the Wallpaper Groups (arXiv:1608.05677)

Last revised on August 30, 2022 at 19:40:06. See the history of this page for a list of all contributions to it.