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tfg_Tormo_Bañuelos_Lucia.pdf (26.41 MB)

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Bachelor thesis

Publication date

2024-06-10

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cc-by-nc-nd (c) Lucía Tormo Bañuelos, 2024
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/220845

Classification of wallpaper groups and frieze groups

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Abstract

The aim of this paper is to classify wallpaper groups and frieze groups. To do so, we will first define symmetry groups and some of their invariants. Then, we will restrict ourselves to plane symmetry groups (the wallpaper groups) and define when two of these groups are equivalent. Then, we will show that there are exactly 17 equivalence classes. We will also see a few examples in order to show how to find the corresponding equivalence class of the wallpaper group for a given periodic design. Moreover, we can also restrict the definition of symmetry groups to frieze groups. Since the defined equivalence relationship will remain valid, we will repeat the same process to see that there are exactly 7 frieze groups, of which we will also study some concrete examples. Finally, we will relate wallpaper groups and frieze groups in the last chapter of this bachelor thesis.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2024, Director: Ricardo García López

Subject

Grups simètrics, Cristal·lografia matemàtica, Grups espacials, Treballs de fi de grau

Subject (English)

Symmetric groups, Mathematical crystallography, Space groups, Bachelor's theses

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

TORMO BAÑUELOS, Lucía. Classification of wallpaper groups and frieze groups. [consulted: 9 of August of 2026]. Available at: https://hdl.handle.net/2445/220845

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