Discrete groups | Euclidean symmetries

Wallpaper group

A wallpaper is a mathematical object covering a whole Euclidean plane by repeating a motif indefinitely, in manner that certain isometries keep the drawing unchanged. To a given wallpaper there corresponds a group of such congruent transformations, with function composition as the group operation. Thus, a wallpaper group (or plane symmetry group or plane crystallographic group) is in a mathematical classification of a two‑dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art, especially in textiles, tessellations and tiles as well as wallpaper. (Wikipedia).

Wallpaper group
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From playlist Beloit College: Ethnomathematics | CosmoLearning.org Mathematics

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Congruence (geometry) | Translational symmetry | Orbifold | Lattice (group) | Glide reflection | Aperiodic tiling | Rational number | Pythagorean theorem | Frieze group | Rotation | Line segment | Square | Dihedral group | Point reflection | Polygon | Sphere | Isometry | Hexagonal tiling | Euclidean space | Similarity (geometry) | Subgroup | Reflection (mathematics) | Truncated hexagonal tiling | Plane (geometry) | Conjugation of isometries in Euclidean space | Rhombus | Symmetry | Degrees of freedom (physics and chemistry) | John Horton Conway | Improper rotation | Mathematical proof | Bravais lattice | Space group | Generating set of a group | Rotational symmetry | Scaling (geometry) | Parallelogram | Coxeter group | Triangular tiling | Snub square tiling | Fundamental domain | Transformation (function) | Discrete space | Hexagon | Mathematics and art | Invariant (mathematics) | Layer group | Isometry group | Identity function | Tetrakis square tiling | Euler characteristic | Concentric objects | Affine transformation | Elongated triangular tiling | Snub trihexagonal tiling | Crystallographic restriction theorem | George Pólya | Function composition | Coxeter notation | Truncated square tiling | Square tiling | Order (group theory) | Translation (geometry) | Point group | Crystallography | Group (mathematics) | Hyperbolic geometry | RGB color model | Tessellation | Orbifold notation | Symmetry group | Trihexagonal tiling | Pythagorean tiling | List of planar symmetry groups | Euclidean plane isometry | Four color theorem | Area | Branko Grünbaum | Rotation (mathematics)