Hexagon
Regular hexagon  

A regular hexagon, {6} 

Edges and vertices  6 
Schläfli symbols  {6} t{3} 
Coxeter–Dynkin diagrams  Image:CDW_ring.pngImage:CDW_ring.png 
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 the Schläfli symbol {6}.
Contents 
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 six 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 artificial
See also
References
 Arnone, Wendy. 2001. Geometry for Dummies. Hoboken, NJ: For Dummies (Wiley). ISBN 0764553240
 Hartshorne, Robin. 2002. Geometry: Euclid and Beyond. Undergraduate Texts in Mathematics. New York, NY: Springer. ISBN 0387986502
 Leff, Lawrence S. 1997. Geometry the Easy Way. Hauppauge, NY: Barron’s Educational Series. ISBN 0764101102
 Stillwell, John. 2005. The Four Pillars of Geometry. Undergraduate Texts in Mathematics. New York, NY: Springer. ISBN 0387255303
External links
All links retrieved June 19, 2013.
 Eric W. Weisstein. Hexagon. 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" Space.com.
Polygons 

Triangle • Quadrilateral • Pentagon • Hexagon • Heptagon • Octagon • Enneagon (Nonagon) • Decagon • Hendecagon • Dodecagon • Triskaidecagon • Pentadecagon • Hexadecagon • Heptadecagon • Enneadecagon • Icosagon • Chiliagon • Myriagon 
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