Hexagon

You don't need to be Editor-In-Chief to add or edit content to WikiDoc. You can begin to add to or edit text on this WikiDoc page by clicking on the edit button at the top of this page. Next enter or edit the information that you would like to appear here. Once you are done editing, scroll down and click the Save page button at the bottom of the page.

Regular hexagon
Image:Hexagon.svg A regular hexagon, {6}
Edges and vertices	6
Schläfli symbols	{6} t{3}
Coxeter–Dynkin diagrams	Image:CDW ring.svgImage:CDW 6.pngImage:CDW dot.svg Image:CDW ring.svgImage:CDW 3.pngImage:CDW ring.svg
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}.

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 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.

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 human-made

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.
• 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)

Template:Polygonsaf:Seshoek ar:سداسي الأضلاع ast:Hexágonu az:Düzgün altıbucaqlı bg:Шестоъгълник ca:Hexàgon cs:Šestiúhelník da:Sekskant de:Sechseckeo:Seslaterogl:Hexágono ko:육각형 it:Esagono he:משושה ht:Egzagòn lt:Šešiakampis hu:Hatszög ms:Heksagon mn:Зургаан өнцөгт nl:Zeshoekno:Heksagon nn:Heksagon nrm:Siêx-carressimple:Hexagon sk:Šesťuholník sl:Šestkotnik sr:Шестоугао fi:Kuusikulmio sv:Hexagon ta:அறுகோணம் te:షడ్భుజి th:รูปหกเหลี่ยม