Euclidean plane tilings by convex regular polygons have been widely used since antiquity. The first systematic mathematical treatment was that of Kepler...

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...

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...

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...

polytopes Hexagonal tiling honeycomb Hex map board game design Tilings and patterns, Sec. 9.3 Other Monohedral tilings by convex polygons Tilings and patterns...

represented by Schläfli symbol {p}. Many sources only consider convex polygons, but star polygons, like the pentagram, when considered, can also be regular. They...

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...

Order-4 square tiling. Checkerboard List of regular polytopes List of uniform tilings Square lattice Tilings of regular polygons Tilings and patterns,...

skew Petrie polygons. The usual five regular polyhedra can also be represented as spherical tilings (tilings of the sphere): For a regular polyhedron whose...

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...

hyperbolic plane, tilings by regular heptagons are possible. There are also concave heptagon tilings possible in the Euclidean plane. The regular heptagon has...

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...

In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are...

Regular Polygons Archived 2015-07-14 at the Wayback Machine, Iowa State University. (retrieved 20 December 2015) Coxeter (1973), Chapter 1, Polygons and...

to cover it entirely. Euclidean tilings by convex regular polygons – a problem of partitioning the entire plane to simple polygons such as rectangles. Squaring...

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...

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...

antiprism) have regular skew hexagons as petrie polygons. The regular skew hexagon is the Petrie polygon for these higher dimensional regular, uniform and...

this is called "grid traversal". Discrete global grid Euclidean tilings by convex regular polygons Geodesic grid Spatial index Grid plan Grid reference...

meet. The classical convex polytopes may be considered tessellations, or tilings, of spherical space. Tessellations of euclidean and hyperbolic space...

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...

regular dodecagon, which is the largest regular polygon that can tessellate space alongside other regular polygons (see, Euclidean tilings by convex regular...

k-uniform tiling is a tiling of tilings of the plane by convex regular polygons, connected edge-to-edge, with k types of vertices. The 1-uniform tiling include...

In Euclidean geometry, a square is a regular quadrilateral, which means that it has four sides of equal length and four equal angles (90-degree angles...

classes can be distinguished: Non-convex cells which pack without overlapping, analogous to tilings of concave polygons. These include a packing of the...

it is a regular polygon. Isogonal polygons are equiangular polygons which alternate two edge lengths. For clarity, a planar equiangular polygon can be...

105–114. Grünbaum, Branko; Shepard, Geoffrey (November 1977). "Tilings by Regular Polygons" (PDF). Mathematics Magazine. 50 (5). Taylor & Francis, Ltd.:...

polyhedra (equivalently, spherical tilings), the square and deltoidal trihexagonal tilings of the Euclidean plane, and some tilings of the hyperbolic plane are...

discovery of new mathematical tile", The Guardian Chavey, D. (1989), "Tilings by Regular Polygons—II: A Catalog of Tilings", Computers & Mathematics with...

may not be convex or even connected. In the usual Euclidean space, we can rewrite the formal definition in usual terms. Each Voronoi polygon R k {\textstyle...