Euclidean tilings by convex regular polygons information

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...

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...

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...

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

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...

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...

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

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...

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

computers could not truly understand such general rules; Euclidean tilings by convex regular polygons, and whether computers could calculate such possibilities;...

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

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

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...

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

least three colors. The cube is the cell of the only regular tiling of three-dimensional Euclidean space. It is also unique among the Platonic solids in...

orientations. The regular dodecahedron is topologically related to a series of tilings by vertex figure n3. The regular dodecahedron can be transformed by a truncation...