Tessellation

A tessellation covers a surface with shapes that fit together without gaps or overlaps. The pattern may repeat periodically or form a nonperiodic arrangement.

Polygon: A closed plane figure bounded by finitely many straight line segments. Polygons are the basic shapes used in many familiar tessellations.
Wallpaper group: One of 17 mathematical groups classifying the symmetries of periodic patterns in the plane. Wallpaper groups classify the repeating symmetries found in periodic tessellations.
Triangular tiling: A regular tiling of the plane by congruent equilateral triangles. Six equilateral triangles meet at every vertex to cover the plane.
Escher tiling: An artistic tessellation whose interlocking tiles often depict recognizable figures. M. C. Escher transformed geometric tilings into images of animals and other forms.
Packing problem: A problem of arranging objects within a region to maximize occupied space or satisfy another objective. Packing permits empty space, whereas a tessellation must cover the surface.
Vertex configuration: A notation describing the sequence of polygon angles meeting at a vertex. It records how the tiles fit around a point in a tessellation.
Translation symmetry: A symmetry in which shifting a pattern by a fixed vector leaves it unchanged. Repeated tiles often reproduce the whole pattern through translations.
Square tiling: A regular tiling of the plane by congruent squares. Four right angles meet at each vertex, producing a familiar periodic pattern.
Islamic geometric patterns: Decorative designs using geometric forms and symmetries across Islamic visual traditions. Many designs use repeating polygonal arrangements closely related to tessellations.
Covering problem: A problem of placing sets so that every point in a region lies in at least one set. Coverings may overlap, unlike the nonoverlapping tiles of a tessellation.

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