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In geometry, the snub infinite-order triangular tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of s{3,∞}. John H. Conway, Heidi
Snub infinite-order triangular tiling
Snub_infinite-order_triangular_tiling
Semiregular tiling of the plane
In geometry, the elongated triangular tiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex
Elongated_triangular_tiling
Symmetric subdivision in hyperbolic geometry
hyperbolic geometry, a uniform hyperbolic tiling (or regular, quasiregular or semiregular hyperbolic tiling) is an edge-to-edge filling of the hyperbolic
Uniform tilings in hyperbolic plane
Uniform_tilings_in_hyperbolic_plane
hyperbolic infinite-order apeirogonal tiling, {∞,∞}, with infinite apeirogonal faces, and with all vertices on the ideal surface. The triangular tiling honeycomb
Triangular_tiling_honeycomb
omnitruncated square tiling honeycomb (or omnisnub square tiling honeycomb), h(t0,1,2,3{4,4,3}), has snub square tiling, snub cube, triangular antiprism, square
Square_tiling_honeycomb
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
Order-4 square tiling honeycomb
Order-4_square_tiling_honeycomb
Subdivision of the plane into polygons that are all regular
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
Euclidean tilings by convex regular polygons
Euclidean_tilings_by_convex_regular_polygons
Geometric operation applied to a polyhedron
degenerate polyhedron, but a valid tiling on the sphere with digon or lune-shaped faces. The same process applies for snub tilings: Nonuniform polyhedra with
Snub_(geometry)
Vertex-transitive tiling of the plane by regular polygons
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
Uniform_tiling
Shape with three equal sides
tessellation's instances are the triangular tiling where six equilateral triangles surrounds a common vertex, and the sphinx tiling as a special case of the polyiamond
Equilateral_triangle
Method of describing higher-order polyhedra
square tiling tQ = bQ Tetrakis square tiling kQ = mQ Snub square tiling sQ Cairo pentagonal tiling gQ Hexagonal tiling H = dΔ = tΔ Trihexagonal tiling aH
Conway_polyhedron_notation
Solid with 10 faces
octagonal antiprism. The square antiprism is first in a series of snub polyhedra and tilings with vertex figure 3.3.4.3.n. If a {\displaystyle a} denotes the
Square_antiprism
contains and that tile 2-hypercycle surfaces, which are similar to the paracompact infinite-order triangular tilings and , respectively: The order-4 octahedral
Order-4_octahedral_honeycomb
Isogonal polyhedron with regular faces
Semiregular polyhedron Polyhedron model Pseudo-uniform polyhedron Uniform tiling Uniform tilings in hyperbolic plane Diudea (2018), p. 40. Coxeter, Longuet-Higgins
Uniform_polyhedron
uniform tilings Uniform tilings in hyperbolic plane Archimedean tiling Square tiling Triangular tiling Hexagonal tiling Truncated square tiling Snub square
List_of_mathematical_shapes
Covering by shapes without overlaps or gaps
Triangular tiling, one of the three regular tilings of the plane Snub hexagonal tiling, a semiregular tiling of the plane Floret pentagonal tiling, dual
Tessellation
Polyhedron; 2 hexagonal pyramids joined base-to-base
with order 2,3,n mirrors at each triangle face vertex. hexagonal trapezohedron A similar 12-sided polyhedron with a twist and kite faces. Snub disphenoid
Hexagonal_bipyramid
Spatial tiling of convex uniform polyhedra
unique honeycombs from the square tiling, but all 6 tiling truncations are listed below for completeness, and tiling images are shown by colors corresponding
Convex_uniform_honeycomb
Classification of a two-dimensional repetitive pattern
one of the colorings of the snub square tiling (see also at pg) 4 co-uniform tiling (fractalization of snub square tiling) Orbifold signature: 333 Coxeter
Wallpaper_group
Tiling of hyperbolic 3-space by uniform polyhedra
small rhombicuboctahedra , infinite order-8 triangular tilings , and infinite order-8 square tilings . The order-8 square tilings already intersect the sphere
Uniform honeycombs in hyperbolic space
Uniform_honeycombs_in_hyperbolic_space
The uniform tilings (infinite polyhedra) 11 Euclidean convex uniform tilings; 28 Euclidean nonconvex or apeirogonal uniform tilings; Infinite number of
List_of_uniform_polyhedra
uniform tilings Uniform tilings in hyperbolic plane Archimedean tiling Square tiling Triangular tiling Hexagonal tiling Truncated square tiling Snub square
List of polygons, polyhedra and polytopes
List_of_polygons,_polyhedra_and_polytopes
the same vertex configuration: see for example Snub order-6 square tiling#Related polyhedra and tiling. A few small convex cases (not involving ideal
List of uniform polyhedra by Schwarz triangle
List_of_uniform_polyhedra_by_Schwarz_triangle
Catalan solid with 120 faces
It has the most faces among the Archimedean and Catalan solids, with the snub dodecahedron, with 92 faces, in second place. If the bipyramids, the gyroelongated
Disdyakis_triacontahedron
Pictorial representation of symmetry
representing a Coxeter group or sometimes a uniform polytope or uniform tiling constructed from the group. A class of closely related objects is the Dynkin
Coxeter–Dynkin_diagram
Isogonal polytope with uniform facets
6 equilateral triangles and is the vertex figure for the regular triangular tiling. Also the cuboctahedron divides into 8 regular tetrahedra and 6 square
Uniform_polytope
Five-dimensional geometric shape
symmetry of order 2304 (2*1152). Three polytopes 85, 86 and 89 (green background) have double symmetry [[3,4,3],2], order 4608. The last one, snub 24-cell
Uniform_5-polytope
Four-dimensional geometric object with flat sides
which tessellate 3-space; similarly the 3D cube is related to the infinite 2D square tiling. Convex 4-polytopes can be cut and unfolded as nets in 3-space
4-polytope
Polyhedron with 12 faces
symmetry of order 10. Snub disphenoid: both Johnson solid and deltahedron, consisting of twelve equilateral triangles. It is D2d of order 8, the same
Dodecahedron
3D shape made of polyhedra sharing a common center
are also dual-regular tiling compounds. A simple example is the E2 compound of a hexagonal tiling and its dual triangular tiling, which shares its edges
Polytope_compound
Antiprism with a five-sided base
In geometry, the pentagonal antiprism is the third in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two
Pentagonal_antiprism
Polyhedron with parallel bases connected by triangles
Antiprisms are a subclass of prismatoids, and are a (degenerate) type of snub polyhedron. Antiprisms are similar to prisms, except that the bases are twisted
Antiprism
Tessellation Uniform tiling Convex uniform honeycombs List of k-uniform tilings List of Euclidean uniform tilings Uniform tilings in hyperbolic plane Weisstein
List_of_tessellations
Convex polyhedron whose faces are almost regular polygons
cases use 4.4.4.4 vertex figures of the square tiling, 3.3.3.3.3.3 vertex figure of the triangular tiling, as well as 60 degree rhombi divided double equilateral
Near-miss_Johnson_solid
Any of the five regular polyhedra
polyhedra: a regular tetrahedron (four triangular faces), a cube (six square faces), a regular octahedron (eight triangular faces), a regular dodecahedron (twelve
Platonic_solid
Four-dimensional analog of the octahedron
Hopf link. The 16 triangle faces can be seen in a 2D net within a triangular tiling, with 6 triangles around every vertex. The purple edges represent
16-cell
Tessellation of convex uniform polyhedron cells
honeycombs with infinite or unbounded facets or vertex figure, including ideal vertices at infinity, similar to the hyperbolic uniform tilings in two dimensions
Paracompact uniform honeycombs
Paracompact_uniform_honeycombs
Flat-sided three-dimensional shape
objects with infinitely many faces. Examples of apeirohedra include tilings or tessellations of the plane, and sponge-like structures called infinite skew polyhedra
Polyhedron
Threshold of percolation theory models
generally a critical surface for a group of parameters p1, p2, ..., such that infinite connectivity (percolation) first occurs. The most common percolation model
Percolation_threshold
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