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...

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...

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...

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

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

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...

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

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

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

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

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

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...

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

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

coincide). Tilings made from planigons can be seen as dual tilings to the regular, semiregular, and demiregular tilings of the plane by regular polygons. In...

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

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

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...

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...

spline B-spline NURBS Parametric surface Convex hull construction Euclidean shortest path Point in polygon Point location Hidden line removal History...

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

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...

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

interior. In this light convex polytopes in p-space are equivalent to tilings of the (p−1)-sphere, while others may be tilings of other elliptic, flat...

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

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