Difference between revisions of "Hexagon" - New World Encyclopedia
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{| border="1" bgcolor="#ffffff" cellpadding="5" align="right" style="margin-left:10px" width="250" | {| border="1" bgcolor="#ffffff" cellpadding="5" align="right" style="margin-left:10px" width="250" | ||
!bgcolor=#e7dcc3 colspan=2|Regular hexagon | !bgcolor=#e7dcc3 colspan=2|Regular hexagon | ||
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|bgcolor=#e7dcc3|[[Schläfli symbol]]s||{6}<BR>t{3} | |bgcolor=#e7dcc3|[[Schläfli symbol]]s||{6}<BR>t{3} | ||
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− | |bgcolor=#e7dcc3|[[Coxeter–Dynkin diagram]]s||[[Image:CDW_ring.png]][[Image:CDW_6.png]][[Image:CDW_dot.png]]<BR> | + | |bgcolor=#e7dcc3|[[Coxeter–Dynkin diagram]]s||[[Image:CDW_ring.png]][[Image:CDW_6.png]][[Image:CDW_dot.png]]<BR>Image:CDW_ring.png[[Image:CDW_3.png]]Image:CDW_ring.png |
|- | |- | ||
|bgcolor=#e7dcc3|[[Symmetry group]]||[[Dihedral symmetry|Dihedral]] (D<sub>6</sub>) | |bgcolor=#e7dcc3|[[Symmetry group]]||[[Dihedral symmetry|Dihedral]] (D<sub>6</sub>) | ||
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Image:Fort-Jefferson Dry-Tortugas.jpg|An aerial view of Fort Jefferson in [[Dry Tortugas National Park]] | Image:Fort-Jefferson Dry-Tortugas.jpg|An aerial view of Fort Jefferson in [[Dry Tortugas National Park]] | ||
Image:Jwst front view.jpg|The [[James Webb Space Telescope]] mirror is composed of 18 hexagonal segments. | Image:Jwst front view.jpg|The [[James Webb Space Telescope]] mirror is composed of 18 hexagonal segments. | ||
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</gallery> | </gallery> | ||
== See also == | == See also == | ||
− | * [[Hexagram]] | + | |
− | * [[ | + | * [[Hexagram]] |
− | * [[ | + | * [[Hexagonal number]] |
− | *[[ | + | * [[Polygon]] |
+ | * [[Square]] | ||
+ | * [[Triangle]] | ||
+ | |||
+ | == References == | ||
+ | '''<<Need at least 3 reliable refs here, properly formatted.>>''' | ||
== External links == | == External links == | ||
+ | |||
* {{MathWorld|title=Hexagon|urlname=Hexagon}} | * {{MathWorld|title=Hexagon|urlname=Hexagon}} | ||
* [http://www.mathopenref.com/hexagon.html Definition and properties of a hexagon] With interactive animation | * [http://www.mathopenref.com/hexagon.html Definition and properties of a hexagon] With interactive animation |
Revision as of 15:01, 2 November 2007
Regular hexagon | |
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250px A regular hexagon, {6} | |
Edges and vertices | 6 |
Schläfli symbols | {6} t{3} |
Coxeter–Dynkin diagrams | File:CDW 6.png Image:CDW_ring.pngImage:CDW_ring.png |
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 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: in nature and by humankind
- Hexa-peri-hexabenzocoronene ChemEurJ 2000 1834.jpg
Crystal structure of a molecular hexagon composed of hexagonal aromatic rings reported by Müllen and coworkers in Chem. Eur. J., 2000, 1834-1839.
See also
ReferencesISBN links support NWE through referral fees
<<Need at least 3 reliable refs here, properly formatted.>>
External links
- 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" - from Space.com (27 March 2007)
Polygons |
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Triangle • Quadrilateral • Pentagon • Hexagon • Heptagon • Octagon • Enneagon (Nonagon) • Decagon • Hendecagon • Dodecagon • Triskaidecagon • Pentadecagon • Hexadecagon • Heptadecagon • Enneadecagon • Icosagon • Chiliagon • Myriagon |
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