AskDefine | Define hexagon

Dictionary Definition

hexagon n : a six-sided polygon

User Contributed Dictionary

English

Noun

  1. A polygon with six sides and six angles.

Translations

A polygon with six sides and six angles
  • Bulgarian: шестоъгълник
  • Czech: šestiúhelník
  • Dutch: zeshoek
  • Finnish: kuusikulmio
  • French: hexagone
  • German: Sechseck
  • Hebrew:
  • Hungarian: hatszög
  • Italian: esagono
  • Japanese: 六角形 ()
  • Portuguese: hexágono
  • Slovak: šesťúholník
  • Spanish: hexágono
  • Swedish: hexagon, sexhörning

Related terms

Extensive Definition

In geometry, a hexagon is a polygon with six edges and six vertices. A regular hexagon has Schläfli symbol .

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 t\,\! is given by A = \fract^2 \simeq 2.598076211 t^2.
The perimeter of a regular hexagon of side length t\,\! is, of course, 6t\,\!, its maximal diameter 2t\,\!, and its minimal diameter t\sqrt\,\!. 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

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

See also

hexagon in Afrikaans: Seshoek
hexagon in Arabic: سداسي الأضلاع
hexagon in Asturian: Hexágonu
hexagon in Azerbaijani: Düzgün altıbucaqlı
hexagon in Bulgarian: Шестоъгълник
hexagon in Catalan: Hexàgon
hexagon in Czech: Šestiúhelník
hexagon in Danish: Sekskant
hexagon in German: Sechseck
hexagon in Spanish: Hexágono
hexagon in Esperanto: Seslatero
hexagon in French: Hexagone
hexagon in Galician: Hexágono
hexagon in Korean: 육각형
hexagon in Italian: Esagono
hexagon in Hebrew: משושה
hexagon in Haitian: Egzagòn
hexagon in Lithuanian: Šešiakampis
hexagon in Hungarian: Hatszög
hexagon in Malay (macrolanguage): Heksagon
hexagon in Mongolian: Зургаан өнцөгт
hexagon in Dutch: Zeshoek
hexagon in Japanese: 六角形
hexagon in Norwegian: Heksagon
hexagon in Norwegian Nynorsk: Heksagon
hexagon in Narom: Siêx-carres
hexagon in Polish: Sześciokąt
hexagon in Portuguese: Hexágono
hexagon in Romanian: Hexagon
hexagon in Russian: Правильный шестиугольник
hexagon in Simple English: Hexagon
hexagon in Slovak: Šesťuholník
hexagon in Slovenian: Šestkotnik
hexagon in Serbian: Шестоугао
hexagon in Finnish: Kuusikulmio
hexagon in Swedish: Hexagon
hexagon in Tamil: அறுகோணம்
hexagon in Telugu: షడ్భుజి
hexagon in Thai: รูปหกเหลี่ยม
hexagon in Turkish: Altıgen
hexagon in Chinese: 六边形
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