Octagon (EntityTopic, 12)
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(polytope explorer integration) |
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| Line 3: | Line 3: | ||
| name=Octagon | | name=Octagon | ||
| dim=2 | | dim=2 | ||
| - | | elements=8, 8 | + | | elements=8 [[digon]]s, 8 [[point]]s |
| genus=0 | | genus=0 | ||
| ssc=G8 | | ssc=G8 | ||
| Line 11: | Line 11: | ||
| extra={{STS Matrix| | | extra={{STS Matrix| | ||
8 0 | 8 0 | ||
| - | 1 1}}{{STS Uniform polytope | + | 1 1}}{{STS Polytope |
| + | | dual=''self-dual'' | ||
| + | | 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> | ||
| - | | schlaefli={8} | + | | schlaefli={8}, t{4} |
| - | | vfigure=[[Digon]], length | + | | 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 == | == Equations == | ||
*The area of a regular octagon with side length ''l'' is: | *The area of a regular octagon with side length ''l'' is: | ||
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 |
