Contents

group theory

# Contents

## Definition

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

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

2. the point group is finite.

## References

e. g.

• 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 February 26, 2019 at 10:29:42. See the history of this page for a list of all contributions to it.