Octagon (EntityTopic, 12)
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- | {{Shape|Octagon| | + | <[#ontology [kind topic] [cats 2D Regular Polytope] [alt [[freebase:01tnyl]] [[wikipedia:Octagon]]]]> |
+ | {{STS Shape | ||
+ | | name=Octagon | ||
+ | | dim=2 | ||
+ | | elements=8 [[digon]]s, 8 [[point]]s | ||
+ | | genus=0 | ||
+ | | ssc=G8 | ||
+ | | ssc2=G8 | ||
+ | | pv_circle=<sup>2√2</sup>⁄<sub>π</sub> ≈ 0.9003 | ||
+ | | pv_square=2(√2-1) ≈ 0.8284 | ||
+ | | extra={{STS Matrix| | ||
+ | 8 0 | ||
+ | 1 1}}{{STS Polytope | ||
+ | | dual=''self-dual'' | ||
+ | | bowers=Oc}}{{STS Uniform polytope | ||
+ | | wythoff=<nowiki>3 | 2 3 or | 2 2 2</nowiki> | ||
+ | | schlaefli={8}, t{4} | ||
+ | | dynkin=x8o, x4x | ||
+ | | vfigure=[[Digon]], length √(2+√2) | ||
+ | }}}} | ||
+ | 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: | ||
+ | <blockquote>(±1, ±(1+√2))</blockquote> | ||
+ | == Equations == | ||
+ | *The area of a regular octagon with side length ''l'' is: | ||
+ | <blockquote>2(1 + √2) {{DotHV}}</blockquote> | ||
- | == | + | == Dissection == |
- | The octagon of side 1 may be [[ | + | The octagon of side 1 may be [[dissect]]ed into 8× isosceles [[triangle]] with sides {1,2×√(1+<sup>√2</sup>⁄<sub>2</sub>)}. |
- | + | <[#polytope [id -8]]> | |
- | + | ||
- | + | ||
{{Dishapes}} | {{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+√2⁄2)}.
Incidence matrix
Usage as facets
- prism: 2× 1-facets of a octagonal prism
- 6× 1-facets of a truncated cube
- 6× 1-facets of a stauropantohedron
- 1× 1-facets of a square cupola
Notable Dishapes | |
Flat: | triangle • square • pentagon • hexagon • octagon • decagon |
Curved: | circle |