In 2-dimensional hyperbolic geometry, the infinite-order hexagonal tiling is a regular tiling. It has Schläfli symbol of {6,∞}. All vertices are ideal...

of the triangular tiling is {3,6}, the vertex figure of this honeycomb is a triangular tiling. Thus, infinitely many hexagonal tilings meet at each vertex...

contains , which tile 2-hypercycle surfaces and are similar to the truncated infinite-order triangular tiling, : The order-4 hexagonal tiling honeycomb is...

paracompact because it has cells composed of an infinite number of faces. Each cell consists of a hexagonal tiling whose vertices lie on a horosphere, a flat...

paracompact because it has cells composed of an infinite number of faces. Each cell is a hexagonal tiling whose vertices lie on a horosphere, a surface...

regular polychora and honeycombs with hexagonal tiling cells. In the geometry of hyperbolic 3-space, the order-3-8 hexagonal honeycomb or (6,3,8 honeycomb) is...

hexadeltille, combining alternate elements from a hexagonal tiling (hextille) and triangular tiling (deltille). Kagome (Japanese: 籠目) is a traditional...

The Schläfli symbol of the order-infinite-3 hexagonal honeycomb is {6,∞,3}, with three infinite-order hexagonal tilings meeting at each edge. The vertex...

along each edge. Its vertex figure is an infinite triangular tiling. Its dual is the order-4 hexagonal tiling honeycomb. A geometric honeycomb is a space-filling...

runcitruncated triangular tiling honeycomb, , has hexagonal tiling, rhombitrihexagonal tiling, triangular prism, and hexagonal prism cells, with an isosceles-trapezoidal...

order-4 apeirogonal tiling {∞,4} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many hexagonal tilings...

boundary) with infinitely many order-8 triangular tilings existing around each vertex in an order-4 hexagonal tiling vertex arrangement. It has a second construction...

beyond the ideal boundary) with four order-6 square tilings existing around each edge and with an order-4 hexagonal tiling vertex figure. It a part of a sequence...

order-5 hexagonal tilings, {6,5}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many hexagonal tilings...

beyond the ideal boundary) with infinitely many triangular tilings existing around each vertex in an order-4 hexagonal tiling vertex arrangement. It has a...

In geometry, the order-3 apeirogonal tiling is a regular tiling of the hyperbolic plane. It is represented by the Schläfli symbol {∞,3}, having three regular...

uniform honeycombs in hyperbolic space List of regular polytopes Infinite-order hexagonal tiling honeycomb Coxeter, Regular Polytopes, 3rd. ed., Dover Publications...

boundary) with infinitely many order-7 triangular tilings existing around each vertex in an order-4 hexagonal tiling vertex arrangement. It has a second construction...

There are eight uniform tilings that can be based from the regular hexagonal tiling (or the dual triangular tiling). Drawing the tiles colored as red on the...

uniform honeycombs in hyperbolic space List of regular polytopes Infinite-order hexagonal tiling honeycomb Coxeter, Regular Polytopes, 3rd. ed., Dover Publications...

tiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex. It is named as a triangular tiling elongated...

must have at least three sides. When considering polyhedra as a spherical tiling, this restriction may be relaxed, since digons (2-gons) can be represented...

In geometry, the hexagonal prism is a prism with hexagonal base. Prisms are polyhedrons; this polyhedron has 8 faces, 18 edges, and 12 vertices. Since...

represents a regular compound tiling. It can also be seen as a subdivision of four hexagonal tilings with each hexagon divided into 12 rhombi. The diagonals...

order-5-3 square honeycomb or 4,5,3 honeycomb a regular space-filling tessellation (or honeycomb). Each infinite cell consists of a pentagonal tiling...

called bihedra, flat polyhedra, or doubly covered polygons. As a spherical tiling, a dihedron can exist as nondegenerate form, with two n-sided faces covering...

vertices with 2 different vertex types, so this tiling would be classed as a ‘3-uniform (2-vertex types)’ tiling. Broken down, 36; 36 (both of different transitivity...

bitruncated hexagonal tiling honeycomb. The runcitruncated order-6 tetrahedral honeycomb is equivalent to the runcicantellated hexagonal tiling honeycomb...

wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An aperiodic tiling uses a small set of tile shapes that cannot form...

colored dodecahedral cells. The order-6 dodecahedral honeycomb is similar to the 2D hyperbolic infinite-order pentagonal tiling, {5,∞}, with pentagonal faces...