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

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...

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...

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...

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

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...

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...

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...

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

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...

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

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

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

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...

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...

edges of the tiling, shown in blue, form an order-3 Cayley tree. Like the Euclidean hexagonal tiling, there are 3 uniform colorings of the order-3 apeirogonal...

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

hexagonal honeycomb is {6,6,3}, with three order-5 hexagonal tilings meeting at each edge. The vertex figure of this honeycomb is a hexagonal tiling,...

order-4 hexagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli symbol of the order-4-3...

regular tilings of the plane. The other two are the square tiling and the hexagonal tiling. There are 9 distinct uniform colorings of a triangular tiling. (Naming...

A hexagonal bipyramid is a polyhedron formed from two hexagonal pyramids joined at their bases. The resulting solid has 12 triangular faces, 8 vertices...

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

Euclidean 3-space) 1 p + 1 q = 1 2 : Euclidean plane tiling 1 p + 1 q < 1 2 : Hyperbolic plane tiling {\displaystyle {\begin{aligned}&{\frac {1}{p}}+{\frac...

hyperbolic 3-space, the order-4 square tiling honeycomb is one of 11 paracompact regular honeycombs. It is paracompact because it has infinite cells and vertex...

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...

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...

Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling is...

by the hexagons of the other tiling into four of the pentagons in the Cairo tiling. Infinitely many different pentagons can form Cairo tilings, all with...