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.

• 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)