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Trihexagonal tiling, the Glossary

In geometry, the trihexagonal tiling is one of 11 uniform tilings of the Euclidean plane by regular polygons.^[1]

56 relations: Arrangement of lines, Atom, Basket weaving, Circle packing, Complex polytope, Coxeter–Dynkin diagram, Crystal structure, Cyclotruncated simplicial honeycomb, Dual polyhedron, Equilateral triangle, Euclidean plane, Euclidean tilings by convex regular polygons, Fundamental domain, Geometrical frustration, Geometry, Harmonices Mundi, Herbertsmithite, Hexagon, Hexagonal tiling, Inuit, Jarosite, Johannes Kepler, John Horton Conway, Kagome metal, Kôdi Husimi, Kissing number, Lath, Lattice (group), List of Euclidean uniform tilings, Mineral, Orbifold notation, Percolation threshold, Quarter cubic honeycomb, Quasiregular polyhedron, Rectification (geometry), Regular polygon, Rhombille tiling, Sachdev–Ye–Kitaev model, Schläfli symbol, Snowshoe, Star of David, Symmetry, Tetrahedron, Triangular prismatic honeycomb, Triangular tiling, Trihexagonal tiling, Truncated tetrahedron, Uniform coloring, Uniform tiling, Vertex (geometry), ... Expand index (6 more) »
Euclidean tilings
Isotoxal tilings
Japanese bamboowork
Quasiregular polyhedra
Semiregular tilings

Arrangement of lines

In geometry, an arrangement of lines is the subdivision of the plane formed by a collection of lines.

See Trihexagonal tiling and Arrangement of lines

Atom

Atoms are the basic particles of the chemical elements.

See Trihexagonal tiling and Atom

Basket weaving

Basket weaving (also basketry or basket making) is the process of weaving or sewing pliable materials into three-dimensional artifacts, such as baskets, mats, mesh bags or even furniture.

See Trihexagonal tiling and Basket weaving

In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap.

See Trihexagonal tiling and Circle packing

Complex polytope

In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one.

See Trihexagonal tiling and Complex polytope

Coxeter–Dynkin diagram

In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing a Coxeter group or sometimes a uniform polytope or uniform tiling constructed from the group.

See Trihexagonal tiling and Coxeter–Dynkin diagram

Crystal structure

In crystallography, crystal structure is a description of ordered arrangement of atoms, ions, or molecules in a crystalline material. Trihexagonal tiling and crystal structure are crystallography.

See Trihexagonal tiling and Crystal structure

Cyclotruncated simplicial honeycomb

In geometry, the cyclotruncated simplicial honeycomb (or cyclotruncated n-simplex honeycomb) is a dimensional infinite series of honeycombs, based on the symmetry of the _n affine Coxeter group.

See Trihexagonal tiling and Cyclotruncated simplicial honeycomb

Dual polyhedron

In geometry, every polyhedron is associated with a second dual structure, where the vertices of one correspond to the faces of the other, and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other.

See Trihexagonal tiling and Dual polyhedron

Equilateral triangle

In geometry, an equilateral triangle is a triangle in which all three sides have the same length.

See Trihexagonal tiling and Equilateral triangle

Euclidean plane

In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted \textbf^2 or \mathbb^2.

See Trihexagonal tiling and Euclidean plane

Euclidean tilings by convex regular polygons

Euclidean plane tilings by convex regular polygons have been widely used since antiquity.

See Trihexagonal tiling and Euclidean tilings by convex regular polygons

Fundamental domain

Given a topological space and a group acting on it, the images of a single point under the group action form an orbit of the action.

See Trihexagonal tiling and Fundamental domain

Geometrical frustration

In condensed matter physics, the term geometrical frustration (or in short: frustration) refers to a phenomenon where atoms tend to stick to non-trivial positions or where, on a regular crystal lattice, conflicting inter-atomic forces (each one favoring rather simple, but different structures) lead to quite complex structures.

See Trihexagonal tiling and Geometrical frustration

Geometry

Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.

See Trihexagonal tiling and Geometry

Harmonices Mundi

Harmonice Mundi (Harmonices mundi libri V)The full title is Ioannis Keppleri Harmonices mundi libri V (The Five Books of Johannes Kepler's The Harmony of the World).

See Trihexagonal tiling and Harmonices Mundi

Herbertsmithite

Herbertsmithite is a mineral with chemical structure ZnCu3(OH)6Cl2.

See Trihexagonal tiling and Herbertsmithite

Hexagon

In geometry, a hexagon (from Greek ἕξ, hex, meaning "six", and γωνία, gonía, meaning "corner, angle") is a six-sided polygon.

See Trihexagonal tiling and Hexagon

Hexagonal tiling

In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex. Trihexagonal tiling and hexagonal tiling are Euclidean tilings and Isogonal tilings.

See Trihexagonal tiling and Hexagonal tiling

Inuit

Inuit (ᐃᓄᐃᑦ 'the people', singular: Inuk, ᐃᓄᒃ, dual: Inuuk, ᐃᓅᒃ; Iñupiaq: Iñuit 'the people'; Greenlandic: Inuit) are a group of culturally and historically similar Indigenous peoples traditionally inhabiting the Arctic and subarctic regions of North America, including Greenland, Labrador, Quebec, Nunavut, the Northwest Territories, Yukon (traditionally), Alaska, and Chukotsky District of Chukotka Autonomous Okrug, Russia.

See Trihexagonal tiling and Inuit

Jarosite

Jarosite is a basic hydrous sulfate of potassium and ferric iron (Fe-III) with a chemical formula of KFe3(SO4)2(OH)6.

See Trihexagonal tiling and Jarosite

Johannes Kepler

Johannes Kepler (27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music.

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John Horton Conway

John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

See Trihexagonal tiling and John Horton Conway

In solid-state physics, the kagome metal or kagome magnet is a type of ferromagnetic quantum material.

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Kôdi Husimi

Kōji Husimi (June 29, 1909 – May 8, 2008, 伏見康治) was a Japanese theoretical physicist who served as the president of the Science Council of Japan.

See Trihexagonal tiling and Kôdi Husimi

Kissing number

In geometry, the kissing number of a mathematical space is defined as the greatest number of non-overlapping unit spheres that can be arranged in that space such that they each touch a common unit sphere.

See Trihexagonal tiling and Kissing number

Lath

A lath or slat is a thin, narrow strip of straight-grained wood used under roof shingles or tiles, on lath and plaster walls and ceilings to hold plaster, and in lattice and trellis work.

See Trihexagonal tiling and Lath

Lattice (group)

In geometry and group theory, a lattice in the real coordinate space \mathbb^n is an infinite set of points in this space with the properties that coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point.

See Trihexagonal tiling and Lattice (group)

List of Euclidean uniform tilings

This table shows the 11 convex uniform tilings (regular and semiregular) of the Euclidean plane, and their dual tilings. Trihexagonal tiling and List of Euclidean uniform tilings are Euclidean tilings.

See Trihexagonal tiling and List of Euclidean uniform tilings

Mineral

In geology and mineralogy, a mineral or mineral species is, broadly speaking, a solid substance with a fairly well-defined chemical composition and a specific crystal structure that occurs naturally in pure form.

See Trihexagonal tiling and Mineral

Orbifold notation

In geometry, orbifold notation (or orbifold signature) is a system, invented by the mathematician William Thurston and promoted by John Conway, for representing types of symmetry groups in two-dimensional spaces of constant curvature.

See Trihexagonal tiling and Orbifold notation

Percolation threshold

The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in random systems.

See Trihexagonal tiling and Percolation threshold

Quarter cubic honeycomb

The quarter cubic honeycomb, quarter cubic cellulation or bitruncated alternated cubic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space.

See Trihexagonal tiling and Quarter cubic honeycomb

Quasiregular polyhedron

In geometry, a quasiregular polyhedron is a uniform polyhedron that has exactly two kinds of regular faces, which alternate around each vertex. Trihexagonal tiling and quasiregular polyhedron are quasiregular polyhedra.

See Trihexagonal tiling and Quasiregular polyhedron

Rectification (geometry)

In Euclidean geometry, rectification, also known as critical truncation or complete-truncation, is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points.

See Trihexagonal tiling and Rectification (geometry)

Regular polygon

In Euclidean geometry, a regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

See Trihexagonal tiling and Regular polygon

Rhombille tiling

In geometry, the rhombille tiling, also known as tumbling blocks, reversible cubes, or the dice lattice, is a tessellation of identical 60° rhombi on the Euclidean plane. Trihexagonal tiling and rhombille tiling are Euclidean tilings, Isotoxal tilings and quasiregular polyhedra.

See Trihexagonal tiling and Rhombille tiling

Sachdev–Ye–Kitaev model

In condensed matter physics and black hole physics, the Sachdev–Ye–Kitaev (SYK) model is an exactly solvable model initially proposed by Subir Sachdev and Jinwu Ye, and later modified by Alexei Kitaev to the present commonly used form.

See Trihexagonal tiling and Sachdev–Ye–Kitaev model

Schläfli symbol

In geometry, the Schläfli symbol is a notation of the form \ that defines regular polytopes and tessellations.

See Trihexagonal tiling and Schläfli symbol

Snowshoe

Snowshoes are specialized outdoor gear for walking over snow.

See Trihexagonal tiling and Snowshoe

Star of David

The Star of David is a generally recognized symbol of both Jewish identity and Judaism.

See Trihexagonal tiling and Star of David

Symmetry

Symmetry in everyday life refers to a sense of harmonious and beautiful proportion and balance.

See Trihexagonal tiling and Symmetry

Tetrahedron

In geometry, a tetrahedron (tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices.

See Trihexagonal tiling and Tetrahedron

Triangular prismatic honeycomb

The triangular prismatic honeycomb or triangular prismatic cellulation is a space-filling tessellation (or honeycomb) in Euclidean 3-space.

See Trihexagonal tiling and Triangular prismatic honeycomb

Triangular tiling

In 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 constituent shapes are not parallelogons. Trihexagonal tiling and triangular tiling are Euclidean tilings and Isogonal tilings.

See Trihexagonal tiling and Triangular tiling

Trihexagonal tiling

In geometry, the trihexagonal tiling is one of 11 uniform tilings of the Euclidean plane by regular polygons. Trihexagonal tiling and trihexagonal tiling are crystallography, Euclidean tilings, Isogonal tilings, Isotoxal tilings, Japanese bamboowork, quasiregular polyhedra and semiregular tilings.

See Trihexagonal tiling and Trihexagonal tiling

References

[1] https://en.wikipedia.org/wiki/Trihexagonal_tiling

Also known as Hexadeltille, Kagome Lattice, Kagome Structure, Kagome crest, Kagome-lattice.

, Vertex configuration, Vertex figure, Wallpaper group, Weaving, Wythoff construction, Wythoff symbol.

Trihexagonal tiling, the Glossary

Table of Contents

See also

Euclidean tilings

Isotoxal tilings

Japanese bamboowork

Quasiregular polyhedra

Semiregular tilings

References