Difference between revisions of "Hexagon" - New World Encyclopedia
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− | { | + | [[Image:Hexagon.png|thumb|250px|A regular hexagon]] |
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+ | In [[geometry]], a '''hexagon''' is a [[polygon]] with six edges and six [[Vertex (geometry)|vertices]]. A regular hexagon has the [[Schläfli symbol]] {6}. | ||
+ | {{toc}} | ||
== Regular hexagon == | == Regular hexagon == | ||
− | [[ | + | The internal [[angle]]s of a regular hexagon (one where all sides and all angles are equal) are all |
+ | 120[[degree (angle)|°]] and the hexagon has 720 degrees. It has six lines of symmetry. Like [[square (geometry)|square]]s and [[equilateral]] [[triangle (geometry)|triangle]]s, regular hexagons fit together without any gaps to ''tile the plane'' (three hexagons meeting at every vertex), and so are useful for constructing [[tessellation]]s. | ||
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The cells of a [[beehive (beekeeping)|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 cells of a [[beehive (beekeeping)|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. | ||
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There is no [[platonic solid]] made of regular hexagons. The [[archimedean solid]]s with some hexagonal faces are the [[truncated tetrahedron]], [[truncated octahedron]], [[truncated icosahedron]] (of [[soccer]] ball and [[fullerene]] fame), [[truncated cuboctahedron]] and the [[truncated icosidodecahedron]]. | There is no [[platonic solid]] made of regular hexagons. The [[archimedean solid]]s 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: | + | ==Hexagons: natural and artificial == |
<gallery> | <gallery> | ||
Image:Honey_comb.jpg|A beehive [[honeycomb]] | Image:Honey_comb.jpg|A beehive [[honeycomb]] | ||
Image:Carapax.svg|The scutes of a turtle's [[carapace]] | Image:Carapax.svg|The scutes of a turtle's [[carapace]] | ||
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Image:Snowflake 300um LTSEM, 13368.jpg|Micrograph of a snowflake | Image:Snowflake 300um LTSEM, 13368.jpg|Micrograph of a snowflake | ||
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Image:Giants causeway closeup.jpg|Naturally formed [[basalt]] columns from [[Giant's Causeway]] in [[Ireland]]; large masses must cool slowly to form a polygonal fracture pattern | Image:Giants causeway closeup.jpg|Naturally formed [[basalt]] columns from [[Giant's Causeway]] in [[Ireland]]; large masses must cool slowly to form a polygonal fracture pattern | ||
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]] | ||
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== See also == | == See also == | ||
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* [[Polygon]] | * [[Polygon]] | ||
− | * [[Square]] | + | * [[Square (geometry)]] |
* [[Triangle]] | * [[Triangle]] | ||
== References == | == References == | ||
− | * Arnone, Wendy. 2001. ''Geometry for Dummies''. Hoboken, NJ: For Dummies (Wiley). ISBN 0764553240 | + | * Arnone, Wendy. 2001. ''Geometry for Dummies''. Hoboken, NJ: For Dummies (Wiley). ISBN 0764553240 |
− | + | * Hartshorne, Robin. 2002. ''Geometry: Euclid and Beyond''. Undergraduate Texts in Mathematics. New York, NY: Springer. ISBN 0387986502 | |
− | * Hartshorne, Robin. 2002. ''Geometry: Euclid and Beyond''. Undergraduate Texts in Mathematics. New York: Springer. ISBN 0387986502 | + | * Leff, Lawrence S. 1997. ''Geometry the Easy Way''. Hauppauge, NY: Barron’s Educational Series. ISBN 0764101102 |
− | + | * Stillwell, John. 2005. ''The Four Pillars of Geometry''. Undergraduate Texts in Mathematics. New York, NY: Springer. ISBN 0387255303 | |
− | * Leff, Lawrence S. 1997. ''Geometry the Easy Way''. Hauppauge, NY: Barron’s Educational Series. ISBN 0764101102 | ||
− | |||
− | * Stillwell, John. 2005. ''The Four Pillars of Geometry''. Undergraduate Texts in Mathematics. New York: Springer. ISBN 0387255303 | ||
== External links == | == External links == | ||
+ | All links retrieved December 24, 2017. | ||
− | * {{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 |
− | *[http://www.nasa.gov/mission_pages/cassini/media/cassini-20070327.html Cassini Images Bizarre Hexagon on Saturn] | + | *[http://www.nasa.gov/mission_pages/cassini/media/cassini-20070327.html Cassini Images Bizarre Hexagon on Saturn] |
− | *[http://www.nasa.gov/mission_pages/cassini/multimedia/pia09188.html Saturn's Strange Hexagon] | + | *[http://www.nasa.gov/mission_pages/cassini/multimedia/pia09188.html Saturn's Strange Hexagon] |
− | * [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1988Icar...76..335G&db_key=AST&data_type=HTML&format= A hexagonal feature around Saturn's North Pole] | + | * [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1988Icar...76..335G&db_key=AST&data_type=HTML&format= A hexagonal feature around Saturn's North Pole] |
− | * [http://space.com/scienceastronomy/070327_saturn_hex.html "Bizarre Hexagon Spotted on Saturn"] | + | * [http://space.com/scienceastronomy/070327_saturn_hex.html "Bizarre Hexagon Spotted on Saturn"] Space.com. |
{{Polygons}} | {{Polygons}} | ||
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[[Category:Physical sciences]] | [[Category:Physical sciences]] | ||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
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{{credit|168510392}} | {{credit|168510392}} |
Latest revision as of 22:56, 12 February 2022
In geometry, a hexagon is a polygon with six edges and six vertices. A regular hexagon has the 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 six 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: natural and artificial
See also
ReferencesISBN links support NWE through referral fees
- Arnone, Wendy. 2001. Geometry for Dummies. Hoboken, NJ: For Dummies (Wiley). ISBN 0764553240
- Hartshorne, Robin. 2002. Geometry: Euclid and Beyond. Undergraduate Texts in Mathematics. New York, NY: Springer. ISBN 0387986502
- Leff, Lawrence S. 1997. Geometry the Easy Way. Hauppauge, NY: Barron’s Educational Series. ISBN 0764101102
- Stillwell, John. 2005. The Four Pillars of Geometry. Undergraduate Texts in Mathematics. New York, NY: Springer. ISBN 0387255303
External links
All links retrieved December 24, 2017.
- 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" Space.com.
Polygons |
---|
Triangle • Quadrilateral • Pentagon • Hexagon • Heptagon • Octagon • Enneagon (Nonagon) • Decagon • Hendecagon • Dodecagon • Triskaidecagon • Pentadecagon • Hexadecagon • Heptadecagon • Enneadecagon • Icosagon • Chiliagon • Myriagon |
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