uniform honeycomb in spherical space. It is also seen as a rectified order-4 square tiling honeycomb, r{4,4,4}: The square tiling honeycomb has three...

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

edge, and infinite octahedra around each vertex in a square tiling vertex figure. A geometric honeycomb is a space-filling of polyhedral or higher-dimensional...

order-4-5 square honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {4,4,5}. It has five square tiling {4,4} around...

hyperbolic geometry, the order-4 hexagonal tiling honeycomb arises as one of 11 regular paracompact honeycombs in 3-dimensional hyperbolic space. It is...

the form {4,3,...,3,4}, starting with the square tiling, {4,4} in the plane. It is one of 28 uniform honeycombs using convex uniform polyhedral cells. Simple...

infinite-order square tiling, r{∞,5} with pentagon and apeirogonal faces. All vertices are on the ideal surface. The truncated order-5 hexagonal tiling honeycomb, t0...

honeycomb has six ideal cubes meeting along each edge. Its vertex figure is an infinite triangular tiling. Its dual is the order-4 hexagonal tiling honeycomb...

field of hyperbolic geometry, the hexagonal tiling honeycomb is one of 11 regular paracompact honeycombs in 3-dimensional hyperbolic space. It is paracompact...

Order-3 icosahedral honeycomb Order-4 octahedral honeycomb Triangular tiling honeycomb Square tiling honeycomb Order-4 square tiling honeycomb Order-6 tetrahedral...

of hyperbolic geometry, the order-6 hexagonal tiling honeycomb is one of 11 regular paracompact honeycombs in 3-dimensional hyperbolic space. It is paracompact...

the tetrahedral-square tiling honeycomb is a paracompact uniform honeycomb, constructed from tetrahedron, cuboctahedron and square tiling cells, in a rhombicuboctahedron...

The triangular tiling honeycomb is one of 11 paracompact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space. It is called paracompact...

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 cubic-square tiling honeycomb is a paracompact uniform honeycomb, constructed from cube and square tiling cells, in a rhombicuboctahedron...

In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane. It has Schläfli symbol of {4,4}, meaning...

hexagonal tiling honeycomb, ↔ Alternated square tiling honeycomb, ↔ (Also quasiregular) Cubic-square tiling honeycomb, Order-4 square tiling honeycomb, =...

an example of the more general mathematical tiling or tessellation in any number of dimensions. Honeycombs are usually constructed in ordinary Euclidean...

tiling or tessellation in any number of dimensions. Its dimension can be clarified as n-honeycomb for a honeycomb of n-dimensional space. Honeycombs are...

is one of three regular tilings of the plane. The other two are the triangular tiling and the square tiling. Hexagonal tiling is the densest way to arrange...

an example of the more general mathematical tiling or tessellation in any number of dimensions. Honeycombs are usually constructed in ordinary Euclidean...

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...

square columns. It is a degenerate honeycomb in Euclidean space, but can be seen as a projection onto the sphere. Its vertex figure, a square tiling is...

Uniform tiling List of uniform tilings Uniform tilings in hyperbolic plane Honeycomb (geometry) Wythoff construction Convex uniform honeycomb List of...

order-5 square tiling, t{4,5}, with truncated square and pentagonal faces: It is similar to the Euclidean (order-4) truncated cubic honeycomb, t{4,3,4}...

tiling honeycomb is {∞,7,3}, with three order-7 apeirogonal tilings meeting at each edge. The vertex figure of this honeycomb is a heptagonal tiling,...

octahedron-hexagonal tiling honeycomb is a paracompact uniform honeycomb, constructed from octahedron, hexagonal tiling, and trihexagonal tiling cells, in a rhombicuboctahedron...

order-5 hexagonal tiling honeycomb. The cantellated order-6 dodecahedral honeycomb, t0,2{5,3,6}, has rhombicosidodecahedron, trihexagonal tiling, and hexagonal...

tiling honeycomb is {∞,8,3}, with three order-8 apeirogonal tilings meeting at each edge. The vertex figure of this honeycomb is an octagonal tiling,...

pentagonal tilings existing around each edge and with an order-5 square tiling vertex figure. It a part of a sequence of regular polychora and honeycombs {p,4...