Hexagon (EntityTopic, 12)

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{{Shape|Hexagon|''No image''|2|6, 6|0|{6}|N/A|[[Line segment|E]][[Triangle|T]]X<sub>1</sub>P|N/A|[[Line segment|Line]], length 2√<sup>5</sup>⁄<sub>4</sub>|N/A|''Self-dual''|N/A|N/A|N/A|none|<sup>3[[Sine values|S<sub>4</sub>]]</sup>⁄<sub>π</sub> ≈ 0.8270|<sup>3[[Sine values|S<sub>4</sub>]]</sup>⁄<sub>4</sub> ≈ 0.6495}}
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<[#ontology [kind topic] [cats 2D Regular Polytope] [alt [[freebase:0g85j]] [[wikipedia:Hexagon]]]]>
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{{STS Shape
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| name=Hexagon
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| dim=2
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| elements=6 [[digon]]s, 6 [[point]]s
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| genus=0
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| ssc=G6
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| ssc2=G6
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| pv_circle=<sup>3[[Sine values|S<sub>4</sub>]]</sup>⁄<sub>π</sub> ≈ 0.8270
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| pv_square=<sup>3[[Sine values|S<sub>4</sub>]]</sup>⁄<sub>4</sub> ≈ 0.6495
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| extra={{STS Matrix|
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6 0
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1 1}}{{STS Polytope
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| 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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}}}}
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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>
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== Segmentation ==
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== Equations ==
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The hexagon of side 1 may be [[segment]]ed into:
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*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.:
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<blockquote><sup>3√3</sup>∕<sub>2</sub> &middot; ''l''<sup>2</sup></blockquote>
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*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.:
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<blockquote><sup>3√3</sup>∕<sub>8</sub> &middot; ''l''<sup>2</sup></blockquote>
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== Dissection ==
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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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*[[Truncated icosahedron]] (20×, 63%)
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*[[Truncated octahedron]] (8×, 57%)
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*[[Truncated tetrahedron]] (4×, 50%)
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{{Dishapes}}
{{Dishapes}}
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[[Category:Regular polygons]]
 

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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