Tessellation is the covering of a surface with one or more geometric shapes so that they fit together with no gaps and no overlaps. A periodic tiling repeats regularly; a regular tessellation uses identical regular-polygon tiles meeting identically at every corner. Only three shapes can tile a plane on their own this way: the equilateral triangle, the square, and the regular hexagon. Semi-regular tessellations combine more than one regular polygon while keeping the same arrangement at every vertex - there are eight of these. Beyond regular and semi-regular tiling, tessellations can also be built from irregular polygons, pentagons, or almost any interlocking shape, as popularised by M. C. Escher's animal- and figure-shaped tiles.
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Tessellation is the covering of a surface with one or more geometric shapes so that they fit together with no gaps and no overlaps. A periodic tiling repeats regularly; a regular tessellation uses identical regular-polygon tiles meeting identically at every corner. Only three shapes can tile a plane on their own this way: the equilateral triangle, the square, and the regular hexagon. Semi-regular tessellations combine more than one regular polygon while keeping the same arrangement at every vertex - there are eight of these. Beyond regular and semi-regular tiling, tessellations can also be built from irregular polygons, pentagons, or almost any interlocking shape, as popularised by M. C. Escher's animal- and figure-shaped tiles.
Tessellated surfaces read as tightly interlocking, edge-to-edge geometry with no visible background - every part of the surface is occupied by a tile. Regular tessellations (triangle, square, hexagon) produce a clean, uniform grid. Semi-regular tessellations introduce more visual complexity while staying orderly. Irregular or interlocking-figure tessellations (in the Escher tradition) read as puzzle-like, with positive and negative space reading as different motifs simultaneously. Where contrasting colours are applied to differently shaped or oriented tiles, the result is a strong graphic, high-contrast surface.
The source treats colour as a separate layer from the tiling structure itself: the same tessellation can be illustrated in a single colour or coloured to make the underlying symmetry (or a different, contrasting pattern) more visible. The four colour theorem guarantees any planar tessellation can be coloured with four colours so that no two adjacent tiles share a colour; producing a colouring that also respects the tessellation's symmetry may require as many as seven colours.
Tessellation has a long decorative history: Sumerian wall decorations used tessellated clay tiles from around 4000 BC, and mosaic tessellations were widely used in classical antiquity. The most decorative historical tradition is Moorish Islamic architecture - Girih and Zellige tilework, seen at the Alhambra and La Mezquita - which is closely associated with regular and semi-regular geometric tiling. M. C. Escher was directly inspired by the Moorish tessellations at the Alhambra after visiting Spain in 1936, and became the artist most associated with figurative (rather than purely geometric) tessellation in graphic art. Tessellated designs also appear in quilting, where interlocking motifs form patchwork shapes, and in origami tessellation, where pleats connect repeating folded units.
Tessellation is the covering of a surface with one or more geometric shapes so that they fit together with no gaps and no overlaps. A periodic tiling repeats regularly; a regular tessellation uses identical regular-polygon tiles meeting identically at every corner.
Tessellated surfaces read as tightly interlocking, edge-to-edge geometry with no visible background - every part of the surface is occupied by a tile. Regular tessellations (triangle, square, hexagon) produce a clean, uniform grid. Semi-regular tessellations introduce more visual complexity while staying orderly.
Textiles and quilting - tessellated designs are used to construct interlocking patchwork motifs in quilts. Tile, mosaic, and architectural surfaces - the source's primary historical application, from ancient mosaic flooring to Moorish wall tiling.
Regular tessellation - one shape only (triangle, square, or hexagon), identical arrangement at every vertex. Semi-regular / Archimedean tessellation - more than one regular polygon, same arrangement of polygons at every vertex; eight variants exist.
g. squares with regular octagons Interlocking figurative tiles (animals, birds, other recognisable forms), most associated with M. C. g. rhombille, Pythagorean tiling) Voronoi-style cellular tessellation, where tiles are irregular convex polygons generated from a set of points
The source treats colour as a separate layer from the tiling structure itself: the same tessellation can be illustrated in a single colour or coloured to make the underlying symmetry (or a different, contrasting pattern) more visible.
Tessellation has a long decorative history: Sumerian wall decorations used tessellated clay tiles from around 4000 BC, and mosaic tessellations were widely used in classical antiquity.
Ogee Pattern, Diamond Pattern, and Check Pattern
