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tessellation
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A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries.
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- Image
- Leeuwarden - Tegeltableau Escher.jpg
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- Commons category
- Tilings
- Commons gallery
- Tiling
- Stack Exchange tag
- mathoverflow.net/tags/tiling
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~27 min read
Article
22 sectionsContents
- History
- Etymology
- Overview
- In mathematics
- Introduction to tessellations
- Wallpaper groups
- Aperiodic tilings
- Tessellations and colour
- Tessellations with polygons
- Voronoi tilings
- Tessellations in higher dimensions
- Tessellations in non-Euclidean geometries
- In art
- In manufacturing
- In nature
- In puzzles and recreational mathematics
- Examples
- See also
- Explanatory footnotes
- References
- Sources
- External links
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries.
A periodic tiling has a repeating pattern. Some special kinds include regular tilings with regular polygonal tiles all of the same shape, and semiregular tilings with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An aperiodic tiling uses a small set of tile shapes that cannot form a repeating pattern (an aperiodic set of prototiles). A tessellation of space, also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions.