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A wallpaper group is a crystallographic group (space group) in dimension 2, hence a subgroup of the isometry group of the Euclidean plane such that
the part of inside the translation group is generated by two linearly independent vectors;
the point group is finite.
John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss: The Symmetries of Things, CRC Press (2008) [ISBN:9781568812205]
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:
Last revised on July 3, 2025 at 12:57:13. See the history of this page for a list of all contributions to it.