AskDefine | Define hexagonal

Dictionary Definition

hexagonal adj : having six sides or divided into hexagons [syn: hexangular]

User Contributed Dictionary

English

Pronunciation

  • /hɛkˈsægənəl/, /hEk"s

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

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