Octagon (EntityTopic, 12)

From Hi.gher. Space

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<[#ontology [kind topic] [cats 2D Regular Polytope] [alt [[freebase:01tnyl]] [[wikipedia:Octagon]]]]>
{{STS Shape
{{STS Shape
| name=Octagon
| name=Octagon
| dim=2
| dim=2
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| elements=8, 8
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| elements=8 [[digon]]s, 8 [[point]]s
| genus=0
| genus=0
| ssc=G8
| ssc=G8
Line 8: Line 9:
| pv_circle=<sup>2√2</sup>⁄<sub>π</sub> ≈ 0.9003
| pv_circle=<sup>2√2</sup>⁄<sub>π</sub> ≈ 0.9003
| pv_square=2(√2-1) ≈ 0.8284
| pv_square=2(√2-1) ≈ 0.8284
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| extra={{STS Rotope
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| extra={{STS Matrix|
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| attrib=none
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8 0
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}}{{STS Uniform polytope
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1 1}}{{STS Polytope
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| dual=''self-dual''
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| bowers=Oc}}{{STS Uniform polytope
| wythoff=<nowiki>3 | 2 3 or | 2 2 2</nowiki>
| wythoff=<nowiki>3 | 2 3 or | 2 2 2</nowiki>
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| schlaefli={8}
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| schlaefli={8}, t{4}
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| vfigure=[[Line segment|Line]], length 1
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| dynkin=x8o, x4x
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| dual=''Self-dual''
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| vfigure=[[Digon]], length √(2+√2)
}}}}
}}}}
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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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== Use ==
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<[#polytope [id -8]]>
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Octagonal faces are found in these trishapes on FGwiki:
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*[[Cubic truncate]] (6×, 63%)
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{{Dishapes}}
{{Dishapes}}
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[[Category:Regular polygons]]
 

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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