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 or star. In the limit, a sequence of regular polygons with an increasing number of...

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...

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...

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

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

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...

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

ISBN 978-0-226-33242-0. Tilings and patterns, Sec. 9.3 Other Monohedral tilings by convex polygons Tilings and patterns, from list of 107 isohedral tilings, pp. 473–481...

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

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

Tilings by Squares". Meeting Alhambra: ISAMA-BRIDGES Conference Proceedings. pp. 265–272. Nelsen, Roger B. (November 2003). "Paintings, plane tilings...

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

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

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...

regular n-dimensional hypercubic honeycombs - {4,3,...,3,4}. These may be treated as infinite polytopes. Hyperbolic tilings and honeycombs (tilings {p...

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

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

monohedral tilings it is denoted [3.6.3.6]. It is also one of 56 possible isohedral tilings by quadrilaterals, and one of only eight tilings of the plane...

is a cube. It can be formed as the convex hull of the six axis-parallel unit vectors in three-dimensional Euclidean space. It is one of the five Platonic...

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...

Face-transitive Cell-transitive Tilings and patterns, Branko Gruenbaum, G. C. Shephard, 1987, 2.5 Tilings using star polygons, pp. 82–85. "duality". maths...

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

figures. In 1926 John Flinders Petrie took the concept of a regular skew polygons, polygons whose vertices are not all in the same plane, and extended...

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...

cross-polytope. The regular octahedron is one of the Platonic solids, a set of convex polyhedra whose faces are congruent regular polygons and the same number...

factors. A tiling or honeycomb of 3-space is the division of three-dimensional Euclidean space into a repetitive grid of polyhedral cells. Such tilings or tessellations...

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

identical meanings, because all uniform polygons must be regular. However, since not all uniform polyhedra are regular, the number of semiregular polytopes...