Octagon (EntityTopic, 12)

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{{Shape|Octagon|''No image''|2|8, 8|0|{8}|N/A|G8|N/A|[[Line segment|Line]], length 1|N/A|''Self-dual''|N/A|N/A|N/A|none|<sup>√2</sup>⁄<sub></sub>|2(√2-1) ≈ 0.8284|N/A|SSC}}
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<[#ontology [kind topic] [cats 2D Regular Polytope] [alt [[freebase:01tnyl]] [[wikipedia:Octagon]]]]>
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{{STS Shape
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| name=Octagon
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| dim=2
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| elements=8 [[digon]]s, 8 [[point]]s
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| genus=0
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| ssc=G8
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| ssc2=G8
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| pv_circle=<sup>2√2</sup>⁄<sub>π</sub> ≈ 0.9003
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| pv_square=2(√2-1) ≈ 0.8284
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| extra={{STS Matrix|
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8 0
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1 1}}{{STS Polytope
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| dual=''self-dual''
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| bowers=Oc}}{{STS Uniform polytope
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| wythoff=<nowiki>3 | 2 3 or | 2 2 2</nowiki>
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| schlaefli={8}, t{4}
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| dynkin=x8o, x4x
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| vfigure=[[Digon]], length √(2+√2)
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}}}}
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An octagon is a polygon with 8 sides. It is the truncated [[square]].
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==Coordinates==
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The coordinates of a regular octagon with side two are all permutations of:
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<blockquote>(±1, ±(1+√2))</blockquote>
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== Equations ==
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*The area of a regular octagon with side length ''l'' is:
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<blockquote>2(1 + √2) {{DotHV}}</blockquote>
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== Segmentation ==
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== Dissection ==
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The octagon of side 1 may be [[segment]]ed into 8× isosceles [[triangle]] with sides {1,2×√(1+<sup>√2</sup>⁄<sub>2</sub>)}.
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The octagon of side 1 may be [[dissect]]ed into 8× isosceles [[triangle]] with sides {1,2×√(1+<sup>√2</sup>⁄<sub>2</sub>)}.
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{{Dishapes}}
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<[#polytope [id -8]]>
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[[Category:Regular polygons]]
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{{Dishapes}}

Latest revision as of 16:05, 26 March 2017

An octagon is a polygon with 8 sides. It is the truncated square.

Coordinates

The coordinates of a regular octagon with side two are all permutations of:

(±1, ±(1+√2))

Equations

  • The area of a regular octagon with side length l is:
2(1 + √2) · l2

Dissection

The octagon of side 1 may be dissected into 8× isosceles triangle with sides {1,2×√(1+√22)}.

Incidence matrix

Dual: Self-dual

#TXIDVaEaTypeName
0 Va= point ;
1 Ea2= digon ;
2 8a88= octagon ;

Usage as facets


Notable Dishapes
Flat: trianglesquarepentagonhexagonoctagondecagon
Curved: circle

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