Euclidean plane tilings by convex regular polygons have been widely used since antiquity. The first systematic mathematical treatment was that of Kepler...
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sides have the same length). Regular polygons may be either convex, star or skew. In the limit, a sequence of regular polygons with an increasing number...
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table shows the 11 convex uniform tilings (regular and semiregular) of the Euclidean plane, and their dual tilings. There are three regular and eight semiregular...
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In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not...
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polytopes Hexagonal tiling honeycomb Hex map board game design Tilings and patterns, Sec. 9.3 Other Monohedral tilings by convex polygons Tilings and patterns...
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represented by Schläfli symbol {p}. Many sources only consider convex polygons, but star polygons, like the pentagram, when considered, can also be regular. They...
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Tessellation (redirect from Euclidean tiling)
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...
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skew Petrie polygons. The usual five regular polyhedra can also be represented as spherical tilings (tilings of the sphere): For a regular polyhedron whose...
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Order-4 square tiling. Checkerboard List of regular polytopes List of uniform tilings Square lattice Tilings of regular polygons Tilings and patterns,...
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Heptagon (redirect from Regular heptagon)
hyperbolic plane, tilings by regular heptagons are possible. There are also concave heptagon tilings possible in the Euclidean plane. The regular heptagon has...
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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...
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Apeirogon (redirect from Regular apeirogons)
and is called the regular apeirogon as defined by H. S. M. Coxeter. A regular apeirogon can be defined as a partition of the Euclidean line E1 into infinitely...
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Platonic solid (redirect from Convex regular polyhedron)
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are...
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Equilateral triangle (redirect from Regular Triangle)
Publications. Grünbaum, Branko; Shepard, Geoffrey (November 1977). "Tilings by Regular Polygons" (PDF). Mathematics Magazine. 50 (5). Taylor & Francis, Ltd.:...
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self-intersecting polygons. Some sources also consider closed polygonal chains in Euclidean space to be a type of polygon (a skew polygon), even when the...
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Square (redirect from Regular quadrilateral)
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four straight sides of equal length and four equal angles (90-degree...
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Digon (redirect from Regular digon)
Regular Polygons Archived 2015-07-14 at the Wayback Machine, Iowa State University. (retrieved 20 December 2015) Coxeter (1973), Chapter 1, Polygons and...
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regular dodecagon, which is the largest regular polygon that can tessellate space alongside other regular polygons (see, Euclidean tilings by convex regular...
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List of mathematical shapes (section Euclidean tilings)
meet. The classical convex polytopes may be considered tessellations, or tilings, of spherical space. Tessellations of euclidean and hyperbolic space...
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In geometry, the truncated square tiling is a semiregular tiling by regular polygons of the Euclidean plane with one square and two octagons on each vertex...
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to cover it entirely. Euclidean tilings by convex regular polygons – a problem of partitioning the entire plane to simple polygons such as rectangles. Squaring...
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Hexagon (redirect from Regular hexagon)
antiprism) have regular skew hexagons as petrie polygons. The regular skew hexagon is the Petrie polygon for these higher dimensional regular, uniform and...
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this is called "grid traversal". Discrete global grid Euclidean tilings by convex regular polygons Geodesic grid Spatial index Grid plan Grid reference...
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Honeycomb (geometry) (redirect from Three-dimensional Euclidean tesselation)
classes can be distinguished: Non-convex cells which pack without overlapping, analogous to tilings of concave polygons. These include a packing of the...
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it is a regular polygon. Isogonal polygons are equiangular polygons which alternate two edge lengths. For clarity, a planar equiangular polygon can be...
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Polyhedron (redirect from Convex polyhedra)
defines a polyhedron as a union of convex polygons (its faces), arranged in space so that the intersection of any two polygons is a shared vertex or edge or...
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geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral...
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Kite (geometry) (section Tilings and polyhedra)
polyhedra (equivalently, spherical tilings), the square and deltoidal trihexagonal tilings of the Euclidean plane, and some tilings of the hyperbolic plane are...
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discovery of new mathematical tile", The Guardian Chavey, D. (1989), "Tilings by Regular Polygons—II: A Catalog of Tilings", Computers & Mathematics with...
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Octahedron (redirect from Regular octahedron)
quasiregular polyhedra and tilings with vertex configurations (3.n)2, progressing from tilings of the sphere to the Euclidean plane and into the hyperbolic...
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