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# Hexagon

In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon. [1]

153 relations: Acute and obtuse triangles, Alternation (geometry), Ancient Greek, Angle, Apothem, Archimedean solid, Aromaticity, Association football, Augmented hexagonal prism, Augmented truncated tetrahedron, Basalt, Beehive, Benzene, Bicentric polygon, Brianchon's theorem, Carapace, Cassini–Huygens, Centroid, Chaim Goodman-Strauss, Chamfer (geometry), Chamfered dodecahedron, Circumscribed circle, Compass-and-straightedge construction, Compression (physics), Concurrent lines, Conic section, Conway criterion, Coronene, Coxeter–Dynkin diagram, Cross-polytope, Crux Mathematicorum, Cube, Cuboid, Cyclic group, Degree (angle), Diagonal, Dihedral group, Directed graph, Dodecagon, Dry Tortugas National Park, Dual polygon, Duality (mathematics), Dynkin diagram, Elongated triangular cupola, Equiangular polygon, Equilateral polygon, Equilateral triangle, Euclid, Euclid's Elements, Euclidean space, ... Expand index (103 more) »

## Acute and obtuse triangles

An acute triangle is a triangle with all three angles acute (less than 90°).

## Alternation (geometry)

In geometry, an alternation or partial truncation, is an operation on a polygon, polyhedron, tiling, or higher dimensional polytope that removes alternate vertices.

## Ancient Greek

The Ancient Greek language includes the forms of Greek used in ancient Greece and the ancient world from around the 9th century BC to the 6th century AD.

## Angle

In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

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## Apothem

The apothem (sometimes abbreviated as apo) of a regular polygon is a line segment from the center to the midpoint of one of its sides.

## Archimedean solid

In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes.

## Aromaticity

In organic chemistry, the term aromaticity is used to describe a cyclic (ring-shaped), planar (flat) molecule with a ring of resonance bonds that exhibits more stability than other geometric or connective arrangements with the same set of atoms.

## Association football

Association football, more commonly known as football or soccer, is a team sport played between two teams of eleven players with a spherical ball.

## Augmented hexagonal prism

In geometry, the augmented hexagonal prism is one of the Johnson solids (J54).

## Augmented truncated tetrahedron

In geometry, the augmented truncated tetrahedron is one of the Johnson solids (J65).

## Basalt

Basalt is a common extrusive igneous (volcanic) rock formed from the rapid cooling of basaltic lava exposed at or very near the surface of a planet or moon.

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## Beehive

A beehive is an enclosed structure man-made in which some honey bee species of the subgenus Apis live and raise their young.

## Benzene

Benzene is an important organic chemical compound with the chemical formula C6H6.

## Bicentric polygon

In geometry, a bicentric polygon is a tangential polygon (a polygon all of whose sides are tangent to an inner incircle) which is also cyclic — that is, inscribed in an outer circle that passes through each vertex of the polygon.

## Brianchon's theorem

In geometry, Brianchon's theorem is a theorem stating that when a hexagon is circumscribed around a conic section, its principal diagonals (those connecting opposite vertices) meet in a single point.

## Carapace

A carapace is a dorsal (upper) section of the exoskeleton or shell in a number of animal groups, including arthropods, such as crustaceans and arachnids, as well as vertebrates, such as turtles and tortoises.

## Cassini–Huygens

The Cassini–Huygens mission, commonly called Cassini, was a collaboration between NASA, the European Space Agency (ESA), and the Italian Space Agency (ASI) to send a probe to study the planet Saturn and its system, including its rings and natural satellites.

## Centroid

In mathematics and physics, the centroid or geometric center of a plane figure is the arithmetic mean position of all the points in the shape.

## Chaim Goodman-Strauss

Chaim Goodman-Strauss (born June 1967 in Austin TX) is an American mathematician who works in convex geometry, especially aperiodic tiling.

## Chamfer (geometry)

In geometry, chamfering or edge-truncation is a topological operator that modifies one polyhedron into another.

## Chamfered dodecahedron

The chamfered dodecahedron is a convex polyhedron with 80 vertices, 120 edges, and 42 faces: 30 hexagons and 12 pentagons.

## Circumscribed circle

In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon.

## Compass-and-straightedge construction

Compass-and-straightedge construction, also known as ruler-and-compass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.

## Compression (physics)

In mechanics, compression is the application of balanced inward ("pushing") forces to different points on a material or structure, that is, forces with no net sum or torque directed so as to reduce its size in one or more directions.

## Concurrent lines

In geometry, three or more lines in a plane or higher-dimensional space are said to be concurrent if they intersect at a single point.

## Conic section

In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.

## Conway criterion

In the mathematical theory of tessellations, the Conway criterion, named for the English mathematician John Horton Conway, describes rules for when a prototile will tile the plane; it consists of the following requirements: The tile must be a closed topological disk with six consecutive points A, B, C, D, E, and F on the boundary such that.

## Coronene

Coronene (also known as superbenzene) is a polycyclic aromatic hydrocarbon (PAH) comprising six peri-fused benzene rings.

## Coxeter–Dynkin diagram

In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes).

## Cross-polytope

In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in n-dimensions.

## Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

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## Cuboid

In geometry, a cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube.

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## Cyclic group

In algebra, a cyclic group or monogenous group is a group that is generated by a single element.

## Degree (angle)

A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, defined so that a full rotation is 360 degrees.

## Diagonal

In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge.

## Dihedral group

In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.

## Directed graph

In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is a set of vertices connected by edges, where the edges have a direction associated with them.

## Dodecagon

In geometry, a dodecagon or 12-gon is any twelve-sided polygon.

## Dry Tortugas National Park

Dry Tortugas National Park is a national park in the United States about west of Key West in the Gulf of Mexico.

## Dual polygon

In geometry, polygons are associated into pairs called duals, where the vertices of one correspond to the edges of the other.

## Duality (mathematics)

In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A. Such involutions sometimes have fixed points, so that the dual of A is A itself.

## Dynkin diagram

In the mathematical field of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double or triple line).

## Elongated triangular cupola

In geometry, the elongated triangular cupola is one of the Johnson solids (J18).

## Equiangular polygon

In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal.

## Equilateral polygon

In geometry, three or more than three straight lines (or segment of a line) make a polygon and an equilateral polygon is a polygon which has all sides of the same length.

## Equilateral triangle

In geometry, an equilateral triangle is a triangle in which all three sides are equal.

## Euclid

Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".

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## Euclid's Elements

The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.

## Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

## Euclidean tilings by convex regular polygons

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

## Extended side

In plane geometry, an extended side or sideline of a polygon is the line that contains one side of the polygon.

## Extremely Large Telescope

The Extremely Large Telescope (ELT) is an astronomical observatory and the world's largest optical/near-infrared extremely large telescope now under construction.

## Fermat number

In mathematics a Fermat number, named after Pierre de Fermat who first studied them, is a positive integer of the form where n is a nonnegative integer.

## Four-dimensional space

A four-dimensional space or 4D space is a mathematical extension of the concept of three-dimensional or 3D space.

## French Guiana

French Guiana (pronounced or, Guyane), officially called Guiana (Guyane), is an overseas department and region of France, on the north Atlantic coast of South America in the Guyanas.

## Fullerene

A fullerene is a molecule of carbon in the form of a hollow sphere, ellipsoid, tube, and many other shapes.

## G2 (mathematics)

In mathematics, G2 is the name of three simple Lie groups (a complex form, a compact real form and a split real form), their Lie algebras \mathfrak_2, as well as some algebraic groups.

## Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

## Giant's Causeway

The Giant's Causeway is an area of about 40,000 interlocking basalt columns, the result of an ancient volcanic fissure eruption.

## Goldberg polyhedron

A Goldberg polyhedron is a convex polyhedron made from hexagons and pentagons.

## Graphene

Graphene is a semi-metal with a small overlap between the valence and the conduction bands (zero bandgap material).

Guadeloupe (Antillean Creole: Gwadloup) is an insular region of France located in the Leeward Islands, part of the Lesser Antilles in the Caribbean.

## Gyroelongated triangular cupola

In geometry, the gyroelongated triangular cupola is one of the Johnson solids (J22).

## Hanksite

Hanksite is a sulfate mineral, distinguished as one of only a handful that contain both carbonate and sulfate ion groups.

## Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 &ndash; March 31, 2003) was a British-born Canadian geometer.

## Hexagonal antiprism

In geometry, the hexagonal antiprism is the 4th in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.

## Hexagonal chess

Hexagonal chess refers to a group of chess variants played on boards composed of hexagon.

## Hexagonal crystal family

In crystallography, the hexagonal crystal family is one of the 6 crystal families, which includes 2 crystal systems (hexagonal and trigonal) and 2 lattice systems (hexagonal and rhombohedral).

## Hexagonal number

A hexagonal number is a figurate number.

## Hexagonal prism

In geometry, the hexagonal prism is a prism with hexagonal base.

## Hexagonal pyramid

In geometry, a hexagonal pyramid is a pyramid with a hexagonal base upon which are erected six triangular faces that meet at a point (the apex).

## Hexagonal tiling

In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which three hexagons meet at each vertex.

## Hexagonal window

Hexagonal window (also Melnikov's or honeycomb window) is a hexagon-shaped window, resembling a bee cell or crystal lattice of graphite.

## Hexagram

A hexagram (Greek) or sexagram (Latin) is a six-pointed geometric star figure with the Schläfli symbol, 2, or.

## Honeycomb

A honeycomb is a mass of hexagonal prismatic wax cells built by honey bees in their nests to contain their larvae and stores of honey and pollen.

## Honeycomb conjecture

The honeycomb conjecture states that a regular hexagonal grid or honeycomb is the best way to divide a surface into regions of equal area with the least total perimeter.

## Icosahedral symmetry

A regular icosahedron has 60 rotational (or orientation-preserving) symmetries, and a symmetry order of 120 including transformations that combine a reflection and a rotation.

## Incircle and excircles of a triangle

In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides.

## Inscribed figure

An inscribed triangle of a circle In geometry, an inscribed planar shape or solid is one that is enclosed by and "fits snugly" inside another geometric shape or solid.

## Intersection

In mathematics, the intersection of two or more objects is another, usually "smaller" object.

## Isogonal figure

In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.

## Isotoxal figure

In geometry, a polytope (for example, a polygon or a polyhedron), or a tiling, is isotoxal or edge-transitive if its symmetries act transitively on its edges.

## James Webb Space Telescope

The James Webb Space Telescope (JWST) is a space telescope developed in collaboration between NASA, the European Space Agency, and the Canadian Space Agency that will be the scientific successor to the Hubble Space Telescope.

## John Horton Conway

John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

## Johnson solid

In geometry, a Johnson solid is a strictly convex polyhedron, which is not uniform (i.e., not a Platonic solid, Archimedean solid, prism, or antiprism), and each face of which is a regular polygon.

## Kite (geometry)

In Euclidean geometry, a kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.

## Lemoine hexagon

In geometry, the Lemoine hexagon is a cyclic hexagon with vertices given by the six intersections of the edges of a triangle and the three lines that are parallel to the edges that pass through its symmedian point.

## Line segment

In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.

## Martinique

Martinique is an insular region of France located in the Lesser Antilles of the West Indies in the eastern Caribbean Sea, with a land area of and a population of 385,551 inhabitants as of January 2013.

## Metabiaugmented hexagonal prism

In geometry, the metabiaugmented hexagonal prism is one of the Johnson solids (J56).

## Metropolitan France

Metropolitan France (France métropolitaine or la Métropole), also known as European France or Mainland France, is the part of France in Europe.

## Northern Ireland

Northern Ireland (Tuaisceart Éireann; Ulster-Scots: Norlin Airlann) is a part of the United Kingdom in the north-east of the island of Ireland, variously described as a country, province or region.

## Octahedral symmetry

A regular octahedron has 24 rotational (or orientation-preserving) symmetries, and a symmetry order of 48 including transformations that combine a reflection and a rotation.

## Octahedron

In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.

## Parabiaugmented hexagonal prism

In geometry, the parabiaugmented hexagonal prism is one of the Johnson solids (J55).

## Parallelogon

A parallelogon is a polygon such that images of the polygon under translations only tile the plane when fitted together along entire sides.

## Parallelohedron

In geometry a parallelohedron is a polyhedron that can tessellate 3-dimensional spaces with face-to-face contacts via translations.

## Pascal's theorem

In projective geometry, Pascal's theorem (also known as the hexagrammum mysticum theorem) states that if six arbitrary points are chosen on a conic (i.e., ellipse, parabola or hyperbola) and joined by line segments in any order to form a hexagon, then the three pairs of opposite sides of the hexagon (extended if necessary) meet in three points which lie on a straight line, called the Pascal line of the hexagon.

## Petrie polygon

In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon in which every (n – 1) consecutive sides (but no n) belongs to one of the facets.

## Platonic solid

In three-dimensional space, a Platonic solid is a regular, convex polyhedron.

## Polygon

In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.

## Polygram (geometry)

In geometry, a generalized polygon can be called a polygram, and named specifically by its number of sides, so a regular pentagram,, has 5 sides, and the regular hexagram, or 2 has 6 sides divided into two triangles.

## Prismatoid

In geometry, a prismatoid is a polyhedron whose vertices all lie in two parallel planes.

## Projection (linear algebra)

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.

Reading is a large, historically important minster town in Berkshire, England, of which it is the county town.

## Reflection symmetry

Reflection symmetry, line symmetry, mirror symmetry, mirror-image symmetry, is symmetry with respect to reflection.

## Regular polygon

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

## Regular polytope

In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.

## Rhombitrihexagonal tiling

In geometry, the rhombitrihexagonal tiling is a semiregular tiling of the Euclidean plane.

## Rhombus

In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a simple (non-self-intersecting) quadrilateral whose four sides all have the same length.

## Rotational symmetry

Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn.

## Saturn

Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter.

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## Schläfli symbol

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

## Simple Lie group

In group theory, a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups.

## Simple polygon

In geometry a simple polygon is a flat shape consisting of straight, non-intersecting line segments or "sides" that are joined pair-wise to form a closed path.

## Skew polygon

In geometry, a skew polygon is a polygon whose vertices are not all coplanar.

## Space.com

Space.com is a space and astronomy news website.

## Square

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.

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## Star polygon

In geometry, a star polygon is a type of non-convex polygon.

## Stellation

In geometry, stellation is the process of extending a polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in n dimensions to form a new figure.

## Symmedian

In geometry, symmedians are three particular geometrical lines associated with every triangle.

## Taiwan

Taiwan, officially the Republic of China (ROC), is a state in East Asia.

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## Tangent

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.

## Tangential polygon

In Euclidean geometry, a tangential polygon, also known as a circumscribed polygon, is a convex polygon that contains an inscribed circle (also called an incircle).

## Tessellation

A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.

## Tetrahedral symmetry

A regular tetrahedron, an example of a solid with full tetrahedral symmetry A regular tetrahedron has 12 rotational (or orientation-preserving) symmetries, and a symmetry order of 24 including transformations that combine a reflection and a rotation.

## The Hexagon

The Hexagon is a multi-purpose theatre and arts venue in Reading, Berkshire, England.

## Theatre

Theatre or theater is a collaborative form of fine art that uses live performers, typically actors or actresses, to present the experience of a real or imagined event before a live audience in a specific place, often a stage.

## Triangle

A triangle is a polygon with three edges and three vertices.

## Triangular cupola

In geometry, the triangular cupola is one of the Johnson solids (J3).

## Triangular hebesphenorotunda

In geometry, the triangular hebesphenorotunda is one of the Johnson solids (J92).

## Triangular prismatic honeycomb

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

## Triangular tiling

In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane.

## Triaugmented hexagonal prism

In geometry, the triaugmented hexagonal prism is one of the Johnson solids (J57).

## Trihexagonal tiling

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

## Truncated cuboctahedron

In geometry, the truncated cuboctahedron is an Archimedean solid, named by Kepler as a truncation of a cuboctahedron.

## Truncated icosahedron

In geometry, the truncated icosahedron is an Archimedean solid, one of 13 convex isogonal nonprismatic solids whose faces are two or more types of regular polygons.

## Truncated icosidodecahedron

In geometry, the truncated icosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces.

## Truncated octahedron

In geometry, the truncated octahedron is an Archimedean solid.

## Truncated tetrahedron

In geometry, the truncated tetrahedron is an Archimedean solid.

## Truncated triakis tetrahedron

The truncated triakis tetrahedron is a convex polyhedron with 16 faces: 4 sets of 3 pentagons arranged in a tetrahedral arrangement, with 4 hexagons in the gaps.

## Truncated trihexagonal tiling

In geometry, the truncated trihexagonal tiling is one of eight semiregular tilings of the Euclidean plane.

## Truncation (geometry)

In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex.

## Unicursal hexagram

The unicursal hexagram is a hexagram or six-pointed star that can be traced or drawn unicursally, in one continuous line rather than by two overlaid triangles.

## Voronoi diagram

In mathematics, a Voronoi diagram is a partitioning of a plane into regions based on distance to points in a specific subset of the plane.

## Voyager 1

Voyager 1 is a space probe launched by NASA on September 5, 1977.

## Wax

Waxes are a diverse class of organic compounds that are lipophilic, malleable solids near ambient temperatures.

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## Zonogon

In geometry, a zonogon is a centrally symmetric convex polygon.

## 24-cell

In geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.

## 3-3 duoprism

In geometry of 4 dimensions, a 3-3 duoprism or triangular duoprism, the smallest p-q duoprism, is a 4-polytope resulting from the Cartesian product of two triangles.

## 5-simplex

In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.

## 6-cube

In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces.

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## References

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