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. For edge in Graph theory, see Edge (graph theory In Geometry, an edge is a one-dimensional Line segment joining In Geometry, a vertex (plural "vertices" is a special kind of point. In Mathematics, the Schläfli symbol is a notation of the form {pqr The Symmetry group of an object ( Image, signal, etc eg in 1D 2D or 3D is the group of all Isometries under which it is In Mathematics, a dihedral group is the group of symmetries of a Regular polygon, including both rotations and reflections Area is a Quantity expressing the two- Dimensional size of a defined part of a Surface, typically a region bounded by a closed Curve. 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 This article describes the unit of angle For other meanings see Degree. Geometry ( Greek γεωμετρία; geo = earth metria = measure is a part of Mathematics concerned with questions of size shape and relative position In Geometry a polygon (ˈpɒlɨɡɒn ˈpɒliɡɒn is traditionally a plane figure that is bounded by a closed path or circuit In Geometry, a vertex (plural "vertices" is a special kind of point. A regular hexagon has Schläfli symbol {6}. In Mathematics, the Schläfli symbol is a notation of the form {pqr

Regular hexagon

A regular hexagon is constructible with compass and straightedge. Pentagon constructgif|thumb|right|Construction of a regular pentagon]] Compass-and-straightedge or ruler-and-compass construction is the construction of lengths or Angles The following is a step-by-step animated method of this, given by Euclid's Elements, Book IV, Proposition 15. Euclid ( Greek:.) fl 300 BC also known as Euclid of Alexandria, is often referred to as the Father of Geometry Euclid's Elements ( Greek:) is a mathematical and geometric Treatise consisting of 13 books written by the Greek

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. In Geometry and Trigonometry, an angle (in full plane angle) is the figure formed by two rays sharing a common Endpoint, called This article describes the unit of angle For other meanings see Degree. It has 6 rotational symmetries and 6 reflection symmetries, making up the dihedral group D₆. Generally speaking an object with rotational symmetry is an object that looks the same after a certain amount of Rotation. Reflection symmetry, line symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is Symmetry with respect In Mathematics, a dihedral group is the group of symmetries of a Regular polygon, including both rotations and reflections 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. Classification A square (regular Quadrilateral) is a special case of a Rectangle as it has four right angles and equal parallel sides In Geometry, an equilateral polygon is a Polygon which has all sides of the same length A triangle is one of the basic Shapes of Geometry: a Polygon with three corners or vertices and three sides or edges which are Line A tessellation or tiling of the plane is a collection of Plane figures that fills the plane with no overlaps and no gaps The cells of a beehive honeycomb are hexagonal for this reason and because the shape makes efficient use of space and building materials. A beehive is in a general sense an enclosed structure in which some species of Honey bees (genus Apis) live and raise their young A honeycomb is a mass of Hexagonal Wax cells built by Honey bees in their nests to contain their larvae and stores of Honey and The Voronoi diagram of a regular triangular lattice is the honeycomb tessellation of hexagons. In Mathematics, a Voronoi diagram, named after Georgy Voronoi, also called a Voronoi Tessellation, a Voronoi decomposition, or

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. In Geometry, a Platonic solid is a convex Regular polyhedron. 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 an Archimedean solid is a highly symmetric semi-regular convex Polyhedron composed of two or more types of Regular polygons meeting The truncated tetrahedron is an Archimedean solid. It has 4 regular Hexagonal faces 4 regular triangular faces 12 vertices and 18 edges The truncated octahedron is an Archimedean solid. It has 8 regular hexagonal faces 6 regular square faces 24 vertices and 36 edges The truncated icosahedron is an Archimedean solid. It comprises 12 regular pentagonal faces 20 regular hexagonal faces 60 vertices and 90 edges Association football, more commonly known as football or soccer, is a Team sport played between two teams of eleven players and is widely considered "C60" and "C-60" redirect here For other uses see C60 (disambiguation. The truncated cuboctahedron is an Archimedean solid. It has 12 regular square faces 8 regular Hexagonal faces 6 regular Octagonal faces 48 vertices The truncated icosidodecahedron is an Archimedean solid. It has 30 regular square faces 20 regular Hexagonal faces 12 regular Decagonal faces

Hexagons: natural and human-made

A beehive honeycomb	The scutes of a turtle's carapace	North polar hexagonal cloud feature on Saturn, discovered by Voyager 1 and confirmed in 2006 by Cassini [1] [2] [3]	Micrograph of a snowflake
Crystal structure of a molecular hexagon composed of hexagonal aromatic rings reported by Müllen and coworkers in Chem. A honeycomb is a mass of Hexagonal Wax cells built by Honey bees in their nests to contain their larvae and stores of Honey and A carapace is a dorsal section of an Exoskeleton or shell in a number of animal groups The Voyager 1 spacecraft is a 722-kilogram robotic Space probe of the outer Solar system and beyond launched September 5, Cassini–Huygens is a joint NASA / ESA / ASI Robotic spacecraft mission currently studying the planet Saturn and its Coronene is a Polycyclic aromatic hydrocarbon consisting of seven peri-fused Benzene rings. Eur. J. , 2000, 1834-1839.	Naturally formed basalt columns from Giant's Causeway in Ireland; large masses must cool slowly to form a polygonal fracture pattern	An aerial view of Fort Jefferson in Dry Tortugas National Park	The James Webb Space Telescope mirror is composed of 18 hexagonal segments. Basalt (bəˈsɔːlt ˈbeisɔːlt ˈbæsɔːlt is a common Extrusive Volcanic rock. The Giant's Causeway (or Clochán na bhFómharach is an area of about 40000 interlocking Basalt columns the result of an ancient volcanic eruption Ireland (pronounced /ˈaɾlənd/ Éire) is the third largest island in Europe, and the twentieth-largest island in the world Dry Tortugas National Park preserves Fort Jefferson and the Dry Tortugas section of the Florida Keys. The James Webb Space Telescope ( JWST) is a planned space Infrared observatory the successor to the aging Hubble Space Telescope.
France has a vaguely hexagonal shape. This article is about the country For a topic outline on this subject see List of basic France topics. In French, "L'hexagone" sometimes refers to the country.

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

External links

• Eric W. Weisstein, Hexagon at MathWorld. For symbols used in the I Ching, see Hexagram (I Ching For a Jewish symbol see Star of David. The unicursal hexagram is a Hexagram or six pointed star that can be traced or drawn Unicursally in one continuous line 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, The n th hexagonal number will be the number of points in a hexagon with n regularly spaced points on a side as Eric W Weisstein (born March 18, 1969, in Bloomington Indiana) is an Encyclopedist who created and maintains MathWorld MathWorld is an online Mathematics reference work created and largely written by Eric W
• 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)