Regular hexagon
A regular hexagon, {6}
Edges and vertices	6
Schläfli symbols	{6} t{3}
Coxeter–Dynkin diagrams
Symmetry group	Dihedral (D6)
Area (with t=edge length)
Internal angle (degrees)	120°

In geometry, a hexagon is a polygon with six edges and six vertices. A regular hexagon has Schläfli symbol {6}. Hexagon can mean: A hexagon is a polygon with 6 sides. ... Image File history File links Hexagon. ... An edge between two vertices For edge in graph theory, see Edge (graph theory) In geometry, an edge is a one-dimensional line segment joining two zero-dimensional vertices in a polytope. ... In geometry, a vertex (plural vertices) is a special kind of point, usually a corner of a polygon, polyhedron, or higher dimensional polytope. ... In mathematics, the Schläfli symbol is a notation of the form {p,q,r,...} that defines regular polytopes and tessellations. ... Coxeter groups in the plane with equivalent diagrams. ... Image File history File links CDW_6. ... Image File history File links CDW_3. ... The symmetry group of an object (e. ... This article deals with three infinite series of point groups in three dimensions which have a symmetry group which as abstract group is a dihedral group Dihn ( n ≥ 2 ). See also point groups in two dimensions. ... This article is about the physical quantity. ... External angles law In geometry, an interior angle (or internal angle) is an angle formed by two sides of a simple polygon that share an endpoint, namely, the angle on the inner side of the polygon. ... This article describes the unit of angle. ... For other uses, see Geometry (disambiguation). ... Look up polygon in Wiktionary, the free dictionary. ... In geometry, a vertex (plural vertices) is a special kind of point, usually a corner of a polygon, polyhedron, or higher dimensional polytope. ... In mathematics, the Schläfli symbol is a notation of the form {p,q,r,...} that defines regular polytopes and tessellations. ...

[edit] Regular hexagon

A regular hexagon is constructible with compass and straightedge. The following is a step-by-step animated method of this, given by Euclid's Elements, Book IV, Proposition 15.

The internal angles of a regular hexagon (one where all sides and all angles are equal) are all 120° and the hexagon has 720 degrees. It has 6 rotational symmetries and 6 reflection symmetries, making up the dihedral group D₆. The longest diagonals of a regular hexagon, connecting diametrically opposite vertices, are twice its sides in length. Like squares and equilateral triangles, regular hexagons fit together without any gaps to tile the plane (three hexagons meeting at every vertex), and so are useful for constructing tessellations. The cells of a beehive honeycomb are hexagonal for this reason and because the shape makes efficient use of space and building materials. The Voronoi diagram of a regular triangular lattice is the honeycomb tessellation of hexagons. Wikipedia does not have an article with this exact name. ... Wikipedia does not have an article with this exact name. ... In mathematics, there are several notions of constructibility: a point in the Euclidean plane that can be constructed with unruled straightedge and compass. ... Creating a regular hexagon with a ruler and compass Construction of a regular pentagon Compass and straightedge or ruler-and-compass construction is the construction of lengths or angles using only an idealized ruler and compass. ... For other uses, see Euclid (disambiguation). ... The frontispiece of Sir Henry Billingsleys first English version of Euclids Elements, 1570 Euclids Elements (Greek: ) is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems... This article is about angles in geometry. ... This article describes the unit of angle. ... The triskelion appearing on the Isle of Man flag. ... Figures with the axes of symmetry drawn in. ... This article may be confusing for some readers, and should be edited to enhance clarity. ... For other uses, see Square. ... In geometry, an equilateral polygon has all sides of the same length. ... For alternate meanings, such as the musical instrument, see triangle (disambiguation). ... A tessellated plane seen in street pavement. ... Domesticated Western honey bees are kept in beehives. ... For other uses, see Honeycomb (disambiguation). ... This is the Voronoi diagram of a random set of points in the plane (all points lie within the image). ...

The area of a regular hexagon of side length is given by

The perimeter of a regular hexagon of side length is, of course, , its maximal diameter , and its minimal diameter .

There is no platonic solid made of regular hexagons. The archimedean solids with some hexagonal faces are the truncated tetrahedron, truncated octahedron, truncated icosahedron (of soccer ball and fullerene fame), truncated cuboctahedron and the truncated icosidodecahedron. In geometry, a Platonic solid is a convex regular polyhedron. ... In geometry an Archimedean solid or semi-regular solid is a semi-regular convex polyhedron composed of two or more types of regular polygon meeting in identical vertices. ... The truncated tetrahedron is an Archimedean solid. ... The truncated octahedron is an Archimedean solid. ... The truncated icosahedron is an Archimedean solid. ... Soccer redirects here. ... The Icosahedral Fullerene C540 C60 and C-60 redirect here. ... A colored model Net (polyhedron) The truncated cuboctahedron is an Archimedean solid. ... The truncated icosidodecahedron, or great rhombicosidodecahedron, is an Archimedean solid. ...

[edit] Hexagons: natural and human-made

A beehive honeycomb Honey Comb Taken by fir0002 File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... For other uses, see Honeycomb (disambiguation). ...	The scutes of a turtle's carapace Image File history File links No higher resolution available. ... The term carapace refers to a dorsal section of an exoskeleton or shell, in a number of animal groups. ...	North polar hexagonal cloud feature on Saturn, discovered by Voyager 1 and confirmed in 2006 by Cassini [1] [2] [3] Image File history File links Size of this preview: 688 × 599 pixel Image in higher resolution (15750 × 13717 pixel, file size: 5. ... Atmospheric characteristics Atmospheric pressure 140 kPa Hydrogen >93% Helium >5% Methane 0. ... For the album by The Verve, see Voyager 1 (album). ... Cassini-Huygens is a joint NASA/ESA/ASI unmanned space mission intended to study Saturn and its moons. ...	Micrograph of a snowflake Image File history File linksMetadata Download high resolution version (8400x6600, 7137 KB) Low temperature scanning electron microscope [1] magnification of a snow crystal. ...
Crystal structure of a molecular hexagon composed of hexagonal aromatic rings reported by Müllen and coworkers in Chem. Eur. J., 2000, 1834-1839. Image File history File linksMetadata Download high-resolution version (664x687, 157 KB) This is a picture generated from crystal structure data reported by Peter T. Herwig, Volker Enkelmann, Oliver Schmelz, Klaus Müllen in Chemistry – A European Journal, Year 2000, Pages 1834-1839. ... Coronene is an aromatic molecule consisting of 7 benzene rings. ...	Naturally formed basalt columns from Giant's Causeway in Ireland; large masses must cool slowly to form a polygonal fracture pattern Close up of Giants Causeway. ... For the cities, see Basalt, Colorado and Basalt, Idaho. ... For other uses, see Giants Causeway (disambiguation). ...	An aerial view of Fort Jefferson in Dry Tortugas National Park Download high resolution version (1200x796, 1037 KB) Fort Jefferson at the Dry Tortugas. ... Dry Tortugas National Park preserves Fort Jefferson and the Dry Tortugas section of the Florida Keys. ...	The James Webb Space Telescope mirror is composed of 18 hexagonal segments. Image File history File links Jwst_front_view. ... The James Webb Space Telescope (JWST) is a planned space infrared observatory, intended to be a significant improvement on the aging Hubble Space Telescope. ...
France has a vaguely hexagonal shape. In French, "L'hexagone" sometimes refers to the country. Scan of Expo67 Coaster for France; This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ...

[edit] See also

• Hexagram: 6-sided star within a regular hexagon
• Unicursal hexagram: single path, 6-sided star, within a hexagon
• Hexagonal tiling: a regular tiling of hexagons in a plane
• Hexagonal number

It has been suggested that Pascals Mystic Hexagram be merged into this article or section. ... The Traditional Unicursal Hexagram The Unicursal Hexagram is a hexagram or six sided and six pointed star that is unique in that it can be traced or drawn as one complete symbol, rather than two overlaid triangles. ... In geometry, the hexagonal tiling is a regular tiling of the Euclidean plane. ... Plane tilings by regular polygons have been widely used since antiquity. ... A hexagonal number is a figurate number that represents a hexagon. ...

[edit] External links

• Eric W. Weisstein, Hexagon at MathWorld.
• Definition and properties of a hexagon With interactive animation
• Cassini Images Bizarre Hexagon on Saturn
• Saturn's Strange Hexagon
• A hexagonal feature around Saturn's North Pole
• "Bizarre Hexagon Spotted on Saturn" - from Space.com (27 March 2007)