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...

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

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...

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

gon. Polygons are primarily classified by the number of sides. Polygons may be characterized by their convexity or type of non-convexity: Convex: any...

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...

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

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...

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

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

aperiodic tilings by towers Andrew Osborne 2018 Two Dimensional symmetry Mutations by Daniel Huson Chavey, D. (1989). "Tilings by Regular Polygons—II: A Catalog...

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...

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

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

both the Euclidean plane and hyperbolic plane. Uniform tilings are related to the finite uniform polyhedra; these can be considered uniform tilings of the...

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...

{\displaystyle n} -dimensional Euclidean space R n {\displaystyle \mathbb {R} ^{n}} . Most texts use the term "polytope" for a bounded convex polytope, and the word...

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

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

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

in Euclidean space is unable to generate uniform tilings alongside other polygons, like the regular pentagon. However, it is one of fourteen polygons that...

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

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...

geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral...