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Hexagon
From Wikipedia, the free encyclopedia
| 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}.
Contents |
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.
 A beehive honeycomb |
 The scutes of a turtle's carapace |
 Micrograph of a snowflake |
|
 Crystal structure of a molecular hexagon composed of hexagonal aromatic rings reported by Müllen and coworkers in Chem. 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. |
 France has a vaguely hexagonal shape. In French, "L'hexagone" sometimes refers to the country. |
- 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
- 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)
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| Triangle · Quadrilateral · Pentagon · Hexagon · Heptagon · Octagon · Enneagon (Nonagon) · Decagon · Hendecagon · Dodecagon · Triskaidecagon · Pentadecagon · Hexadecagon · Heptadecagon · Enneadecagon · Icosagon · Chiliagon · Myriagon |