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Uniform tiling of the hyperbolic plane
In geometry, the cantic order-4 hexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1{(4,4,3)} or h2{6,4}. John
Cantic order-4 hexagonal tiling
Cantic_order-4_hexagonal_tiling
composed of triangular tiling and octahedron cells, in a truncated octahedron vertex figure. The cantic order-4 hexagonal tiling honeycomb, ↔ , is composed
Order-4 hexagonal tiling honeycomb
Order-4_hexagonal_tiling_honeycomb
is a quasiregular honeycomb. The cantic order-5 hexagonal tiling honeycomb, h2{6,3,5}, ↔ , has trihexagonal tiling, truncated icosahedron, and icosidodecahedron
Order-5 hexagonal tiling honeycomb
Order-5_hexagonal_tiling_honeycomb
a hexagonal tiling vertex figure. The cantic order-6 hexagonal tiling honeycomb is a lower-symmetry construction of the rectified triangular tiling honeycomb
Order-6 hexagonal tiling honeycomb
Order-6_hexagonal_tiling_honeycomb
rectified order-4 hexagonal tiling honeycomb, t1{4,4,4}, has square tiling facets, with a cubic vertex figure. It is the same as the regular square tiling honeycomb
Order-4 square tiling honeycomb
Order-4_square_tiling_honeycomb
figure. The cantic square tiling honeycomb, h2{4,4,3}, is a paracompact uniform honeycomb in hyperbolic 3-space. It has truncated square tiling, truncated
Square_tiling_honeycomb
a cantic order-6 square tiling, h2{4,6} By *663 symmetry, this tiling can be constructed as an omnitruncation, t{(6,6,3)}: The dual to this tiling represent
Truncated order-6 hexagonal tiling
Truncated_order-6_hexagonal_tiling
constructed as a cantic order-6 hexagonal tiling honeycomb, ↔ . A second lower-index construction is ↔ . The truncated triangular tiling honeycomb, , is
Triangular_tiling_honeycomb
Tiling of a plane by regular hexagons and equilateral triangles
second is called a cantic hexagonal tiling, h2{6,3}, with two colors of triangles, existing in p3m1 (*333) symmetry. The trihexagonal tiling can be used as
Trihexagonal_tiling
Semiregular tiling of the Euclidean plane
the rhombitrihexagonal tiling is a semiregular tiling of the Euclidean plane. There are one triangle, two squares, and one hexagon on each vertex. It has
Rhombitrihexagonal_tiling
Regular tiling of hyperbolic 3-space
forms: the cantic order-5 cubic honeycomb, , the runcic order-5 cubic honeycomb, , and the runcicantic order-5 cubic honeycomb, . The cantic order-5 cubic
Order-5_cubic_honeycomb
Quasiregular space-filling tesselation
by the symmetry of rings in the Coxeter–Dynkin diagrams: The cantic cubic honeycomb, cantic cubic cellulation or truncated half cubic honeycomb is a uniform
Tetrahedral-octahedral honeycomb
Tetrahedral-octahedral_honeycomb
Archimedean solid with 26 faces
below as spherical tilings. For p < 6, they are tilings of the hyperbolic plane, starting with the truncated triheptagonal tiling. It is first in a series
Truncated_cuboctahedron
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
Tessellation of convex uniform polyhedron cells
graphs: [(3,3,4,1+,4)] = [((3,∞,3)),((3,∞,3))] or , [(3,4,4,1+,4)] = [((4,∞,3)),((3,∞,4))] or , [(4,4,4,1+,4)] = [((4,∞,4)),((4,∞,4))] or . = , = , =
Paracompact uniform honeycombs
Paracompact_uniform_honeycombs
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
Only regular space-filling tessellation of the cube
which is around 4.3% greater than the other. The snub cubes in this case are uniform, but the rest of the cells are not. The cantic snub cubic honeycomb
Cubic_honeycomb
Archimedean solid with 8 faces
has 4 regular hexagonal faces, 4 equilateral triangle faces, 12 vertices and 18 edges (of two types). It can be constructed by truncating all 4 vertices
Truncated_tetrahedron
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
honeycomb) in Euclidean 4-space. It is constructed by a bitruncation of a tesseractic honeycomb. It is also called a cantic quarter tesseractic honeycomb
Bitruncated tesseractic honeycomb
Bitruncated_tesseractic_honeycomb
Isogonal polytope with uniform facets
For example, the regular hexagon divides into 6 equilateral triangles and is the vertex figure for the regular triangular tiling. Also the cuboctahedron
Uniform_polytope
Five-dimensional geometric shape
family has symmetry of order 28800 (2*14400). Uniform duoprism prisms, {p}×{q}×{ }, form an infinite class for all integers p,q>2. {4}×{4}×{ } makes a lower
Uniform_5-polytope
truncated 16-cell honeycomb (or cantic tesseractic honeycomb) is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed
Truncated_16-cell_honeycomb
Municipality in Andalusia, Spain
Tableros ("Gate of the Boards"), and all that remains of it is one of its hexagonal towers with fragments of its large horseshoe archway. This minaret is
Granada
List for England, retrieved 7 July 2019 Historic England, "Nos. 2, 3 and 4 The Close, Lichfield (1298426)", National Heritage List for England, retrieved
Listed_buildings_in_Lichfield
Uniform 6-dimensional polytope
family has symmetry of order 51,840. Uniform triaprisms, {p}×{q}×{r}, form an infinite class for all integers p,q,r>2. {4}×{4}×{4} makes a lower symmetry
Uniform_6-polytope
Architectural styles
elements of the building. For example, the typical brick and roof tile construction, hexagonal turrets, ornate gable work, finials, prominent verandah, steep
Australian residential architectural styles
Australian_residential_architectural_styles
Baroque architectural style from Sicily
or a hexagon, typical of Renaissance and Baroque town planning. The city of Grammichele is an example of these new cities rebuilt to a hexagonal plan
Sicilian_Baroque
Historic England & 1375837. Historic England & 1375923. Hubbard (1991), pp. 4–5, 56–58. Historic England & 1375759. Morris & Roberts (2012), pp. 61–62.
Grade II listed buildings in Chester (east)
Grade_II_listed_buildings_in_Chester_(east)
Subprefecture and commune in Provence-Alpes-Côte d'Azur, France
The wooden furniture, the stalls, the pulpit and the lectern with its hexagonal base, form an interesting 18th and 19th-century set, some of which is
Castellane
districts were abolished in 1974. The Local Government (Successor Parishes) Order 1973 merged all four parishes into one new successor civil parish called
Listed_buildings_in_Sleaford
Mills on the River Medway, Kent, England
pit wheel with oak cogs. This drove a cast iron wallower on a wooden hexagonal upright shaft, driving a wooden Great Spur Wheel 8 feet (2.44 m) in diameter
Medway watermills (upper tributaries)
Medway_watermills_(upper_tributaries)
for England, retrieved 25 May 2016 Historic England, "West City Walls and Tile Tower adjoining at south-west, Carlisle (1197002)", National Heritage List
Listed_buildings_in_Carlisle
Retrieved 19 February 2013. Historic England. "Exton House, Walls and Railings 4, Second Avenue, BN3 2LL, Brighton (Grade II) (1209667)". National Heritage
Grade II listed buildings in Brighton and Hove: E–H
Grade_II_listed_buildings_in_Brighton_and_Hove:_E–H
Historic England. Retrieved 22 January 2026. "Listed Building 1064652 - 4 Lamp Standards at North End". Historic England. Retrieved 23 January 2026
Grade II listed buildings in the City of London (EC4)
Grade_II_listed_buildings_in_the_City_of_London_(EC4)
retrieved 4 May 2021 Historic England, "Grand Arcade, City and Hunslet Ward (1375223)", National Heritage List for England, retrieved 4 May 2021 Historic
Listed buildings in Leeds (City and Hunslet Ward - northern area)
Listed_buildings_in_Leeds_(City_and_Hunslet_Ward_-_northern_area)
Elphin, Warrington (1329734)", National Heritage List for England, retrieved 4 October 2015 More, Warrington Parish Church, retrieved 10 February 2013 Pollard
Listed buildings in Warrington (unparished area)
Listed_buildings_in_Warrington_(unparished_area)
4 Belgrave Terrace, Huddersfield (1134416)", National Heritage List for England, retrieved 13 October 2020 Historic England, "Gate piers to No. 4 Belgrave
Listed buildings in Huddersfield (Newsome Ward - outer areas)
Listed_buildings_in_Huddersfield_(Newsome_Ward_-_outer_areas)
CANTIC ORDER-4-HEXAGONAL-TILING
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