the truncated infinite-order triangular tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of t{3,∞}. The dual of this tiling represents...

and that tile 2-hypercycle surfaces, which are similar to the paracompact tilings and (the truncated infinite-order triangular tiling and order-3 apeirogonal...

hyperbolic truncated order-3 apeirogonal tiling, t{∞,3} with apeirogonal and triangle faces: The bitruncated hexagonal tiling honeycomb or bitruncated order-6...

order-4 hexagonal tiling honeycomb, ↔ , is composed of trihexagonal tiling, truncated cuboctahedron, truncated cube, and triangular prism cells, with...

honeycomb, {4,4,3}, . The truncated order-4 square tiling honeycomb, t0,1{4,4,4}, has square tiling and truncated square tiling facets, with a square pyramid...

The cantitruncated order-5 hexagonal tiling honeycomb, t0,1,2{6,3,5}, has truncated icosahedron, truncated trihexagonal tiling, and pentagonal prism...

geometry, 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...

2t{4,4,3}, has truncated cube and truncated square tiling facets, with a digonal disphenoid vertex figure. The cantellated square tiling honeycomb, rr{4...

constructed as a cantic order-6 hexagonal tiling honeycomb, ↔ . A second lower-index construction is ↔ . The truncated triangular tiling honeycomb, , is a lower-symmetry...

the truncated order-3 apeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of t{∞,3}. The dual tiling, the infinite-order...

hexagonal tiling and a regular triangular tiling. Two hexagons and two triangles alternate around each vertex, and its edges form an infinite arrangement...

The truncated trihexagonal tiling has three related 2-uniform tilings, one being a 2-uniform coloring of the semiregular rhombitrihexagonal tiling. The...

honeycombs with triangular tiling vertex figures. The rectified order-6 tetrahedral honeycomb, t1{3,3,6} has octahedral and triangular tiling cells arranged...

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...

has media related to Uniform dual tiling V 4-6-14. In geometry, the 3-7 kisrhombille tiling is a semiregular dual tiling of the hyperbolic plane. It is constructed...

tessellation of the truncated square tiling which has one square and two octagons at each vertex. A 5 × 9 portion of the tetrakis square tiling is used to form...

modified in the same manner as the other polyhedra to produce a truncated variation. The truncated n-gonal hosohedron is the n-gonal prism. In the limit, the...

square tiling honeycomb. The runcitruncated order-4 octahedral honeycomb, t0,1,3{3,4,4}, has truncated octahedron, hexagonal prism, and square tiling facets...

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...

regular triangular tiling). A tiling can also be self-dual. The square tiling, with Schläfli symbol {4,4}, is self-dual; shown here are two square tilings (red...

hyperbolic geometry, a uniform hyperbolic tiling (or regular, quasiregular or semiregular hyperbolic tiling) is an edge-to-edge filling of the hyperbolic...

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...

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...

part of a sequence of honeycombs with a square tiling vertex figure: The {2,4,4} honeycomb can be truncated as t{2,4,4} or {}×{4,4}, Coxeter diagram , seen...

wedge vertex figure. The cantitruncated order-5 dodecahedral honeycomb, , has truncated icosidodecahedron, truncated icosahedron, and pentagonal prism cells...

uniform tilings Uniform tilings in hyperbolic plane Archimedean tiling Square tiling Triangular tiling Hexagonal tiling Truncated square tiling Snub square...

octahedra (as triangular antiprisms). Its vertex figure is an order-3 truncated triakis tetrahedron. This honeycomb is the dual of the triakis truncated tetrahedral...

Each vertex is ideal, and surrounded by infinitely many dodecahedra. The honeycomb has a triangular tiling vertex figure. A geometric honeycomb is a...

antiprism, D6d symmetry, order 24 Triakis tetrahedron – 12 isosceles triangles, dual of truncated tetrahedron, Td symmetry, order 24 Other less regular faced:...

the five truncations of the Platonic solids—truncated tetrahedron, truncated octahedron, truncated cube, truncated dodecahedron, and truncated icosahedron—and...