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Regular tiling of a two-dimensional space
one of three regular tilings of the plane. The other two are the triangular tiling and the square tiling. The hexagonal tiling has a structure consisting
Hexagonal_tiling
Semiregular tiling of a plane
In geometry, the truncated hexagonal tiling is a semiregular tiling of the Euclidean plane. There are 2 dodecagons (12-sides) and one triangle on each
Truncated_hexagonal_tiling
Regular paracompact honeycomb
symbol of the hexagonal tiling honeycomb is {6,3,3}. Since that of the hexagonal tiling is {6,3}, this honeycomb has three such hexagonal tilings meeting at
Hexagonal_tiling_honeycomb
the order-4 hexagonal tiling honeycomb is {6,3,4}. Since that of the hexagonal tiling is {6,3}, this honeycomb has four such hexagonal tilings meeting at
Order-4 hexagonal tiling honeycomb
Order-4_hexagonal_tiling_honeycomb
Uniform tiling of the Euclidean plane
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
Truncated_trihexagonal_tiling
Shape with six sides
Hexagonal crystal system Hexagonal number Hexagonal tiling: a regular tiling of hexagons in a plane Hexagram: six-sided star within a regular hexagon
Hexagon
the order-5 hexagonal tiling honeycomb is {6,3,5}. Since that of the hexagonal tiling is {6,3}, this honeycomb has five such hexagonal tilings meeting at
Order-5 hexagonal tiling honeycomb
Order-5_hexagonal_tiling_honeycomb
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
Order-6 hexagonal tiling honeycomb
Order-6_hexagonal_tiling_honeycomb
Map subdivided into a hexagonal tiling, small regular hexagons of identical size
games and video games. A hex map is subdivided into a hexagonal tiling, small regular hexagons of identical size. The primary advantage of a hex map over
Hex_map
Regular tiling of the hyperbolic plane
geometry, the order-4 hexagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {6,4}. This tiling represents a hyperbolic
Order-4_hexagonal_tiling
Covering by shapes without overlaps or gaps
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
Tessellation
Regular tiling of the hyperbolic plane
the order-6 hexagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {6,6} and is self-dual. This tiling represents a
Order-6_hexagonal_tiling
Semiregular tiling of the Euclidean plane
the snub hexagonal tiling (or snub trihexagonal tiling) is a semiregular tiling of the Euclidean plane. There are four triangles and one hexagon on each
Snub_trihexagonal_tiling
nonwythoffian Hexagonal tiling – 3 colorings, all wythoffian Trihexagonal tiling – 2 colorings, both wythoffian Snub square tiling – 2 colorings
List of Euclidean uniform tilings
List_of_Euclidean_uniform_tilings
Tiling of the plane with 60° rhombi
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
Rhombille_tiling
Tiling of the plane by pentagons
can tile the plane. Their tilings have varying symmetries; all are face-symmetric. One particular form of the tiling, dual to the snub square tiling, has
Cairo_pentagonal_tiling
Regular tiling of the Euclidean plane
properties, the square tiling is categorized as one of three regular tilings; the remaining being triangular tiling and hexagonal tiling with its prototiles
Square_tiling
Regular tiling of the plane
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
Triangular_tiling
Geometric operation which truncates the edges of polyhedra
and hexagonal faces. Its dual is the alternate-triakis tetratetrahedron. chamfered cube: from a cube, the resulting polyhedron has twelve hexagonal and
Chamfer_(geometry)
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
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
Tiling of a plane by regular hexagons and equilateral triangles
hexadeltille, combining alternate elements from a hexagonal tiling (hextille) and triangular tiling (deltille). Kagome (Japanese: 籠目) is a traditional
Trihexagonal_tiling
runcitruncated triangular tiling honeycomb, , has hexagonal tiling, rhombitrihexagonal tiling, triangular prism, and hexagonal prism cells, with an isosceles-trapezoidal
Triangular_tiling_honeycomb
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
List_of_regular_polytopes
3-space, the hexagonal tiling-triangular tiling honeycomb is a paracompact uniform honeycomb, constructed from triangular tiling, hexagonal tiling, and trihexagonal
Hexagonal tiling-triangular tiling honeycomb
Hexagonal_tiling-triangular_tiling_honeycomb
icosahedron Square tiling Triangular tiling Hexagonal tiling Apeirogon Dihedron Lobachevski plane Hyperbolic tiling Order-7 heptagrammic tiling Heptagrammic-order
List_of_mathematical_shapes
One of the five 2D Bravais lattices
lattice (see dots in a diagonal square centered) Hexagonal tiling Close-packing Centered hexagonal number Eisenstein integer Voronoi diagram Hermite
Hexagonal_lattice
Theorem about infinite graphs
with thick ends are exactly the graphs containing subdivisions of the hexagonal tiling of the plane. It was published by Rudolf Halin (1965), and is a precursor
Halin's_grid_theorem
(or honeycomb) in Euclidean 3-space made up of hexagonal prisms. It is constructed from a hexagonal tiling extruded into prisms. It is one of 28 convex
Triangular prismatic honeycomb
Triangular_prismatic_honeycomb
Pattern in hyperbolic geometry
In geometry, the truncated order-4 hexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t{6,4}. A secondary construction
Truncated order-4 hexagonal tiling
Truncated_order-4_hexagonal_tiling
octahedron-hexagonal tiling honeycomb is a paracompact uniform honeycomb, constructed from octahedron, hexagonal tiling, and trihexagonal tiling cells, in
Octahedral-hexagonal tiling honeycomb
Octahedral-hexagonal_tiling_honeycomb
beyond the ideal boundary) with seven hexagonal tilings existing around each edge and with an order-7 triangular tiling vertex figure. It a part of a sequence
Order-3-7_hexagonal_honeycomb
Zigzagging chevron pattern
the herringbone pattern is topologically identical to the regular hexagonal tiling. This can be seen if the rectangular blocks are distorted slightly
Herringbone_pattern
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
In geometry, the truncated order-6 hexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t{6,6}. It can also be identically
Truncated order-6 hexagonal tiling
Truncated_order-6_hexagonal_tiling
geometry, the alternated hexagonal tiling honeycomb, h{6,3,3}, or , is a semiregular tessellation with tetrahedron and triangular tiling cells arranged in an
Alternated hexagonal tiling honeycomb
Alternated_hexagonal_tiling_honeycomb
Classification of a two-dimensional repetitive pattern
hexagonal tiling with one color for outlining the hexagons and one for the background. Examples of group p6m Computer generated Trihexagonal tiling Small
Wallpaper_group
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
Semiregular tiling of the plane
tiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex. It is named as a triangular tiling elongated
Elongated_triangular_tiling
Tiling of the hyperbolic plane
In geometry, the heptagonal tiling is a regular tiling of the hyperbolic plane. It is represented by Schläfli symbol of {7,3}, having three regular heptagons
Heptagonal_tiling
Type of tabletop game using tiles
exist with square tiles, triangular tiles and even hexagonal tiles. Modern games may use unconventional non-tileable shapes such as the curved-shaped Bendominoes
Tile-based_game
In 2-dimensional hyperbolic geometry, the infinite-order hexagonal tiling is a regular tiling. It has Schläfli symbol of {6,∞}. All vertices are ideal
Infinite-order hexagonal tiling
Infinite-order_hexagonal_tiling
Shape with three equal sides
hexagonal tiling, rhombitrihexagonal tiling, trihexagonal tiling, snub square tiling, and snub hexagonal tiling are all semi-regular tessellations constructed
Equilateral_triangle
Polyform with a regular hexagon as the base form
a regular hexagonal tiling. The rules for joining hexagons together may vary. Generally, however, the following rules apply: Two hexagons may be joined
Polyhex
Polyhedron with two kinds of faces
continues as the trihexagonal tiling, vertex figure (3.6)2 - a quasiregular tiling based on the triangular tiling and hexagonal tiling. The checkerboard pattern
Quasiregular_polyhedron
Uniform tiling of the hyperbolic plane
In geometry, the alternated order-4 hexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of (3,4,4), h{6,4}, and hr{6,6}
Alternated order-4 hexagonal tiling
Alternated_order-4_hexagonal_tiling
Uniform tiling of the plane with regular polygons
generates a truncated hexagonal tiling, while the 3.4.3.12 only exists in this 2-uniform tiling. There are 2 3-uniform tilings that contain both of these
3-4-3-12_tiling
Polyhedron with 2 faces
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
Dihedron
Tiling of the plane by pentagons
geometry, a pentagonal tiling is a tiling of the plane where each individual piece is in the shape of a pentagon. A regular pentagonal tiling on the Euclidean
Pentagonal_tiling
Mathematical theorem
{\displaystyle \Gamma } per unit area is at least as large as for the hexagon tiling. The theorem applies even if the complement of Γ {\displaystyle \Gamma
Honeycomb_theorem
Notation for a polyhedron's vertex figure
6 (60) Regular tilings: Hexagonal tiling: 6.6.6 Semiregular tilings: Truncated hexagonal tiling: 3.12.12 Truncated trihexagonal tiling: 4.6.12 Truncated
Vertex_configuration
Periodic tiling of the hyperbolic disk
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
Order-3_apeirogonal_tiling
Infinite regular skew polyhedron
Euclidean tilings and 3 skew honeycombs): Triangular tiling: {3, 6} Square tiling: {4, 4} Hexagonal tiling: {6, 3} Petrial triangular tiling: {3, 6}π Petrial
Regular_skew_apeirohedron
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
triangular tiling vertex figures. The rectified order-6 tetrahedral honeycomb, t1{3,3,6} has octahedral and triangular tiling cells arranged in a hexagonal prism
Order-6_tetrahedral_honeycomb
Uniform tiling of the hyperbolic plane
tiling, r{6,4}, as well as an expanded order-4 hexagonal tiling or expanded order-6 square tiling. There are two uniform constructions of this tiling
Rhombitetrahexagonal_tiling
Polyhedron with regular congruent polygons as faces
paracompact regular honeycombs have Euclidean tiling facets and vertex figures that act like finite polyhedra. Such tilings have an angle defect that can be closed
Regular_polyhedron
In geometry, the truncated order-5 hexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1{6,5}. John H. Conway, Heidi
Truncated order-5 hexagonal tiling
Truncated_order-5_hexagonal_tiling
Semiregular tiling of the hyperbolic plane
truncated order-8 hexagonal tiling is a semiregular tiling of the hyperbolic plane. It has Schläfli symbol of t{6,8}. This tiling can also be constructed
Truncated order-8 hexagonal tiling
Truncated_order-8_hexagonal_tiling
Isogonal polytope with regular facets
order-6 hexagonal tiling honeycomb, ↔ Alternated square tiling honeycomb, ↔ (quasiregular) Cubic-square tiling honeycomb, Order-4 square tiling honeycomb
Semiregular_polytope
Question about single-shape aperiodic tiling
Binary tiling, a weakly aperiodic tiling of the hyperbolic plane with a single tile Schmitt–Conway–Danzer tile, in three dimensions Two tiles have the
Einstein_problem
Polyhedron; 2 hexagonal pyramids joined base-to-base
A hexagonal bipyramid is a polyhedron formed from two hexagonal pyramids joined at their bases. The resulting solid has 12 triangular faces, 8 vertices
Hexagonal_bipyramid
vertex in an octagonal tiling vertex figure. It is a part of a sequence of regular honeycombs with order-8 triangular tiling cells: {3,8,p}. It is a
Order-8-3 triangular honeycomb
Order-8-3_triangular_honeycomb
Regular space-filling tessellation
tilings existing around each edge and with an order-5 hexagonal tiling vertex figure. In the geometry of hyperbolic 3-space, the order-6-6 hexagonal honeycomb
Order-6-4_square_honeycomb
Regular geometrical object in hyperbolic space
order-5 hexagonal tiling honeycomb. The order-6 dodecahedral honeycomb is part of a sequence of regular polychora and honeycombs with triangular tiling vertex
Order-6 dodecahedral honeycomb
Order-6_dodecahedral_honeycomb
Geometric operation applied to a polyhedron
honeycomb is the snub hexagonal tiling honeycomb, as s{3,6,3} and , which can also be constructed as an alternated hexagonal tiling honeycomb, h{6,3,3}
Snub_(geometry)
Mathematics book
topics in tiling theory: colored patterns and tilings, polygonal tilings, aperiodic tilings, Wang tiles, and tilings with unusual kinds of tiles. Each chapter
Tilings_and_patterns
Road surface built with hexagonal tiles
of each hexagonal blocks were to be coated with resin and the blocks were laid tightly together on a sand-and-gravel bed in the hexagonal tiling—the gaps
Trylinka
Regular tiling of the hyperbolic plane
square tiling, t{4,8}. Like the hexagonal tiling of the Euclidean plane, there are 3 uniform colorings of this hyperbolic tiling. The dual tiling V8.8.8
Octagonal_tiling
Polygon able to tessellate edge-to-edge, without rotation
a distorted square tiling while a hexagonal parallelogon can tile the plane as a distorted regular hexagonal tiling. Aleksandr Danilovich Alexandrov (2005)
Parallelogon
Semi-regular arrangement of squares, decagons, and dodecagons
In geometry, the truncated tetrahexagonal tiling is a semiregular tiling of the hyperbolic plane. There are one square, one decagon, and one dodecagon
Truncated pentahexagonal tiling
Truncated_pentahexagonal_tiling
Semiregular tiling of the hyperbolic plane
related to Uniform tiling 3-14-14. Truncated hexagonal tiling Heptagonal tiling Tilings of regular polygons List of uniform tilings John H. Conway, Heidi
Truncated_heptagonal_tiling
Field of geometry closely arranging circles on a plane
lattice packing of circles is the hexagonal packing arrangement, in which the centres of the circles are arranged in a hexagonal lattice (staggered rows, like
Circle_packing
2003 video game
2003 tile-matching puzzle video game developed by Carbonated Games for various platforms. In Hexic, the player tries to rotate hexagonal tiles to create
Hexic
honeycombs with order-7 triangular tiling cells: {3,7,p}. It is a part of a sequence of regular honeycombs with heptagonal tiling vertex figures: {p,7,3}. In
Order-7-3 triangular honeycomb
Order-7-3_triangular_honeycomb
6,3}, with three order-4 hexagonal tilings meeting at each edge. The vertex figure of this honeycomb is a hexagonal tiling, {6,3}. It is a part of a
Order-6-3_square_honeycomb
Method of describing higher-order polyhedra
Euclidean tilings can also be used as seeds: Q = Quadrille = Square tiling H = Hextille = Hexagonal tiling = dΔ Δ = Deltille = Triangular tiling = dH These
Conway_polyhedron_notation
Type of video game
rectangular, parallelogram, or hexagonal) graphic images referred to as tiles laid out in a grid. That the screen is made of such tiles is a technical distinction
Tile-based_video_game
k-uniform tiling is a tiling of tilings of the plane by convex regular polygons, connected edge-to-edge, with k types of vertices. The 1-uniform tiling include
List_of_k-uniform_tilings
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
Group realized geometrically by reflections across the sides of a triangle
centrally symmetric. Hence each of them determines a tiling of the real projective plane, an elliptic tiling. Its symmetry group is the quotient of the spherical
Triangle_group
duals: There are at least 5 polygonal tilings of the Euclidean plane that are isotoxal. (The self-dual square tiling recreates itself in all four forms.)
List of isotoxal polyhedra and tilings
List_of_isotoxal_polyhedra_and_tilings
Semiregular tiling of the hyperbolic plane
In geometry, the truncated tetrahexagonal tiling is a semiregular tiling of the hyperbolic plane. There are one square, one octagon, and one dodecagon
Truncated tetrahexagonal tiling
Truncated_tetrahexagonal_tiling
Convex polygon which can tile the plane by itself
Laves tilings are unique except for the square tiling (1 degree of freedom), barn pentagonal tiling (1 degree of freedom), and hexagonal tiling (2 degrees
Planigon
Regular tiling of the hyperbolic plane
geometry, the order-6 square tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {4,6}. This tiling represents a hyperbolic kaleidoscope
Order-6_square_tiling
Organic molecule whose carbon structure is a Platonic solid
can also be extended to regular Euclidean tilings, with the hexagonal tiling producing graphane. A square tiling (which would resemble an infinitely large
Platonic_hydrocarbon
Non-periodic tiling of the plane
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
Penrose_tiling
Aperiodic tile
triangle-like tiling that occurs), with rotations and reflections of the tile allowed. It is the first known example of a single aperiodic tile, or "einstein"
Socolar–Taylor_tile
(Increasing any of the numbers defining a hyperbolic or Euclidean tiling makes another hyperbolic tiling.) Point groups: (p 2 2) dihedral symmetry, p = 2 , 3 , 4
Lists of uniform tilings on the sphere, plane, and hyperbolic plane
Lists_of_uniform_tilings_on_the_sphere,_plane,_and_hyperbolic_plane
Natural number
can uniformly tile the plane alongside other regular polygons, as with the truncated hexagonal tiling or the truncated trihexagonal tiling. A regular dodecahedron
12_(number)
truncated order-6 square tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t{4,6}. The dual tiling represents the fundamental
Truncated order-6 square tiling
Truncated_order-6_square_tiling
Collection of wax cells built by honeybees
exist as to why honeycomb is composed of hexagons rather than any other shape. First, the hexagonal tiling creates a partition with equal-sized cells
Honeycomb
Rule from the theory of the tiling of the plane
periodic tiling of the plane—and does so using only 180-degree rotations. The Conway criterion is a sufficient condition to prove that a prototile tiles the
Conway_criterion
Semiregular tiling of the hyperbolic plane
tiling 3-3-3-3-7. Snub hexagonal tiling Floret pentagonal tiling Order-3 heptagonal tiling Tilings of regular polygons List of uniform planar tilings
Snub_triheptagonal_tiling
Math theorem about sphere packing
circle packing. The hexagonal honeycomb theorem The most efficient partition of the plane into equal areas is the regular hexagonal tiling. Related to Thue's
Kepler_conjecture
Shape subdivided into copies of itself
shape necessarily forms the prototile for a tiling of the plane, in many cases a nonperiodic tiling. A rep-tile dissection using different sizes of the original
Rep-tile
Polygon with 18 edges
concave hexagonal gaps. And another tiling mixes in nonagons and octagonal gaps. The first tiling is related to a truncated hexagonal tiling, and the
Octadecagon
many triangular tilings existing around each vertex in an order-4 hexagonal tiling vertex arrangement. It has a second construction as a uniform honeycomb
Order-6-4 triangular honeycomb
Order-6-4_triangular_honeycomb
Semiregular tiling of the hyperbolic plane
truncated triangular tiling, sometimes called the hyperbolic soccerball, is a semiregular tiling of the hyperbolic plane. There are two hexagons and one heptagon
Truncated order-7 triangular tiling
Truncated_order-7_triangular_tiling
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 hexagonal honeycomb
Order-4-3 pentagonal honeycomb
Order-4-3_pentagonal_honeycomb
HEXAGONAL TILING
HEXAGONAL TILING
Surname or Lastname
English and Irish
English and Irish : unexplained; most probably a habitational name from a lost or unidentified place somewhere in South Wales or southern England. This name was established in County Meath, Ireland, soon after the Anglo-Norman invasion of the 12th century.Dutch : unexplained.Probably a respelling of German Tiling, a patronymic form of Thiel.
HEXAGONAL TILING
HEXAGONAL TILING
HEXAGONAL TILING
HEXAGONAL TILING
HEXAGONAL TILING
HEXAGONAL TILING
HEXAGONAL TILING