Hexagon
Background Information
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Regular hexagon  

A regular hexagon, {6} 

Edges and vertices  6 
Schläfli symbols  {6} t{3} 
Coxeter–Dynkin diagrams  
Symmetry group  Dihedral (D_{6}) 
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}.
Regular hexagon
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 lines of symmetry. 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.
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.
Hexagons: natural and humanmade

Hexaperihexabenzocoronene ChemEurJ 2000 1834.jpg
Crystal structure of a molecular hexagon composed of hexagonal aromatic rings reported by Müllen and coworkers in Chem. Eur. J., 2000, 18341839.

Naturally formed basalt columns from Giant's Causeway in Ireland; large masses must cool slowly to form a polygonal fracture pattern

France has a vaguely hexagonal shape. In French, "L'hexagone" sometimes refers to the country.