"Tessellate" redirects here. For the song, see Tessellate (song). For the computer graphics technique, see Tessellation (computer graphics).
"Mathematical tiling" redirects here. For the building material, see Mathematical tile.
Zellige terracotta tiles in Marrakech, forming edge‑to‑edge, regular and other tessellations
A wall sculpture in Leeuwarden celebrating the artistic tessellations of M. C. Escher
An example of non‑periodicity due to another orientation of one tile out of an infinite number of identical tiles
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.
A real physical tessellation is a tiling made of materials such as cemented ceramic squares or hexagons. Such tilings may be decorative patterns, or may have functions such as providing durable and water-resistant pavement, floor, or wall coverings. Historically, tessellations were used in Ancient Rome and in Islamic art such as in the Moroccan architecture and decorative geometric tiling of the Alhambra palace. In the twentieth century, the work of M. C. Escher often made use of tessellations, both in ordinary Euclidean geometry and in hyperbolic geometry, for artistic effect. Tessellations are sometimes employed for decorative effect in quilting. Tessellations form a class of patterns in nature, for example in the arrays of hexagonal cells found in honeycombs.
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...
close to each of a given set of objects. It can be classified also as a tessellation. In the simplest case, these objects are just finitely many points in...
A uniform tessellation may be: A uniform tiling in two dimensions A uniform honeycomb in higher dimensions This disambiguation page lists articles associated...
vertex shader is called for each vertex in a primitive (possibly after tessellation); thus one vertex in, one (updated) vertex out. Each vertex is then rendered...
In geometry, an edge tessellation is a partition of the plane into non-overlapping polygons (a tessellation) with the property that the reflection of any...
Voronoi tessellations of five points in a square In geometry, a centroidal Voronoi tessellation (CVT) is a special type of Voronoi tessellation in which...
generate a covered plane given the notation alone. And second, some tessellations have the same nomenclature, they are very similar but it can be noticed...
hexagons meeting at every vertex), and so are useful for constructing tessellations. The cells of a beehive honeycomb are hexagonal for this reason and...
the density or intensity of points samplings by means of the Delaunay tessellation field estimator (DTFE). Delaunay triangulations are often used to generate...
classified in Schwarz (1873). These can be defined more generally as tessellations of the sphere, the Euclidean plane, or the hyperbolic plane. Each Schwarz...
In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex...
In geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral...
the very strict constraints. Origami tessellation is a branch that has grown in popularity after 2000. A tessellation is a collection of figures filling...
In mathematics, the E8 lattice is a special lattice in R8. It can be characterized as the unique positive-definite, even, unimodular lattice of rank 8...
\chi =2-k} .[citation needed] The simplest tessellation in two-dimensional space, though an improper tessellation, is that of two ∞ {\displaystyle \infty...
In applied mathematics, a Gilbert tessellation or random crack network is a mathematical model for the formation of mudcracks, needle-like crystals, and...
John Horton Conway defines architectonic and catoptric tessellations as the uniform tessellations (or honeycombs) of Euclidean 3-space with prime space...
products: hardware tessellation with TeraScale. Support for hardware tessellation only became mandatory in Direct3D 11 and OpenGL 4. Tessellation as defined in...
An aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic regions or patches. A set...
Archimedean Tessellations) Wikimedia Commons has media related to Uniform tilings of the hyperbolic plane. Hatch, Don. "Hyperbolic Planar Tessellations". Retrieved...
angle of 90°. The tesseract's radial equilateral symmetry makes its tessellation the unique regular body-centered cubic lattice of equal-sized spheres...
In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane. It has Schläfli symbol of {4,4}, meaning...
to give a (n − j)-dimensional element. The dual of an n-dimensional tessellation or honeycomb can be defined similarly. In general, the facets of a polytope's...
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