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Example tessellation based on a Type 1 hexagonal tile. In its simplest form, the criterion simply states that any hexagon with a pair of opposite sides that are parallel and congruent will tessellate the plane. [8] In Gardner's article, this is called a type 1 hexagon. [7] This is also true of parallelograms.
The fundamental region is a shape such as a rectangle that is repeated to form the tessellation. [22] For example, a regular tessellation of the plane with squares has a meeting of four squares at every vertex. [18] The sides of the polygons are not necessarily identical to the edges of the tiles.
Download as PDF; Printable version; In other projects Wikidata item; ... This is a list of tessellations. This list is incomplete; you can help by adding missing items.
Tessellations of euclidean and hyperbolic space may also be considered regular polytopes. Note that an 'n'-dimensional polytope actually tessellates a space of one dimension less. For example, the (three-dimensional) platonic solids tessellate the 'two'-dimensional 'surface' of the sphere.
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. It has Schläfli symbol of {6,3} or t {3,6} (as a truncated triangular tiling).
Algebra and Tiling: Homomorphisms in the Service of Geometry is a mathematics textbook on the use of group theory to answer questions about tessellations and higher dimensional honeycombs, partitions of the Euclidean plane or higher-dimensional spaces into congruent tiles.
In geometry, a domino tiling of a region in the Euclidean plane is a tessellation of the region by dominoes, shapes formed by the union of two unit squares meeting edge-to-edge. Equivalently, it is a perfect matching in the grid graph formed by placing a vertex at the center of each square of the region and connecting two vertices when they ...
In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane, and is the only such tiling where the constituent shapes are not parallelogons. Because the internal angle of the equilateral triangle is 60 degrees, six triangles at a point occupy a full 360 degrees.
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