Hexagon (EntityTopic, 12)

From Hi.gher. Space

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<[#ontology [kind topic] [cats 2D Regular Flat Shape]]>
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<[#ontology [kind topic] [cats 2D Regular Polytope] [alt [[freebase:0g85j]] [[wikipedia:Hexagon]]]]>
{{STS Shape
{{STS Shape
| name=Hexagon
| name=Hexagon
| dim=2
| dim=2
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| elements=6, 6
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| elements=6 [[digon]]s, 6 [[point]]s
| genus=0
| genus=0
| ssc=G6
| ssc=G6
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| extra={{STS Matrix|
| extra={{STS Matrix|
  6 0
  6 0
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  1 1}}{{STS Uniform polytope
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  1 1}}{{STS Polytope
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| schlaefli={6}
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| vfigure=[[Digon]], length 2√<sup>5</sup>⁄<sub>4</sub>
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| dual=''Self-dual''
| dual=''Self-dual''
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| bowers=Hig
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}}{{STS Uniform polytope
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| schlaefli={6}, t{3}
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| dynkin=x6o, x3x
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| vfigure=[[Digon]], length √3
}}}}
}}}}
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A hexagon is a 6-sided polygon. It is also the truncated [[triangle]]. It is one of the regular polygons that can tile the plain.
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==Coordinates==
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The coordinates of a regular hexagon of side 2 are:
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<blockquote>(±1, ±√3)<br>(0, ±2)</blockquote>
== Equations ==
== Equations ==
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<blockquote><sup>3√3</sup>∕<sub>8</sub> &middot; ''l''<sup>2</sup></blockquote>
<blockquote><sup>3√3</sup>∕<sub>8</sub> &middot; ''l''<sup>2</sup></blockquote>
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== Segmentation ==
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== Dissection ==
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The hexagon of side 1 may be [[segment]]ed into:
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The hexagon of side 1 may be [[dissect]]ed into:
*6× equilateral [[triangle]] with side 1
*6× equilateral [[triangle]] with side 1
*3× [[rhombus]] with angles 2×{60°,120°}
*3× [[rhombus]] with angles 2×{60°,120°}
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== Use ==
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<[#polytope [id -6]]>
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Hexagonal faces are found in these trishapes on FGwiki:
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*[[Icosahedral truncate]] (20×, 63%)
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*[[Octahedral truncate]] (8×, 57%)
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*[[Tetrahedral truncate]] (4×, 50%)
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*[[Hexagonal prism]] (2×, 25%)
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{{Dishapes}}
{{Dishapes}}

Latest revision as of 15:56, 26 March 2017

A hexagon is a 6-sided polygon. It is also the truncated triangle. It is one of the regular polygons that can tile the plain.

Coordinates

The coordinates of a regular hexagon of side 2 are:

(±1, ±√3)
(0, ±2)

Equations

  • The area of a regular hexagon with side length l is equal to six times the area of an equilateral triangle with side length l, i.e.:
3√32 · l2
  • Because the diameter of a hexagon is twice its side length, the area of a hexagon with diameter l is a quarter of this, i.e.:
3√38 · l2

Dissection

The hexagon of side 1 may be dissected into:

  • 6× equilateral triangle with side 1
  • rhombus with angles 2×{60°,120°}

Incidence matrix

Dual: Self-dual

#TXIDVaEaTypeName
0 Va= point ;
1 Ea2= digon ;
2 6a66= hexagon ;

Usage as facets


Notable Dishapes
Flat: trianglesquarepentagonhexagonoctagondecagon
Curved: circle

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