Pentagon (EntityTopic, 12)

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The '''pentagon''' can be seen as the two-dimensional analog to the [[dodecahedron]] in 3D and the [[cosmochoron]] in 4D. It is also the lowest-dimensional member of the [[ursatope]]s, with a (trivial) [[digon]]al base.
The '''pentagon''' can be seen as the two-dimensional analog to the [[dodecahedron]] in 3D and the [[cosmochoron]] in 4D. It is also the lowest-dimensional member of the [[ursatope]]s, with a (trivial) [[digon]]al base.
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==coordinates==
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The coordinates of a regular pentagon centered at the origi and having side length 2 are:
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<blockquote>(√((10+2√5)/5), 0)<br>(√((5-√5)/10), ±φ)<br>√((5+2√5)/5), ±1)</blockquote>
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Where φ is the golden ratio (1+√5)/2.
== Equations ==
== Equations ==
*The [[hypervolume]]s of a pentagon with side length ''l'' are given by:
*The [[hypervolume]]s of a pentagon with side length ''l'' are given by:

Latest revision as of 14:25, 26 March 2017

The pentagon can be seen as the two-dimensional analog to the dodecahedron in 3D and the cosmochoron in 4D. It is also the lowest-dimensional member of the ursatopes, with a (trivial) digonal base.

coordinates

The coordinates of a regular pentagon centered at the origi and having side length 2 are:

(√((10+2√5)/5), 0)
(√((5-√5)/10), ±φ)
√((5+2√5)/5), ±1)

Where φ is the golden ratio (1+√5)/2.

Equations

  • The hypervolumes of a pentagon with side length l are given by:
total edge length = 5l
area = 1∕4 · √(25+10√5) · l2

Incidence matrix

Dual: Self-dual

#TXIDVaEaTypeName
0 Va= point ;
1 Ea2= digon ;
2 5a55= pentagon ;

Usage as facets


Notable Dishapes
Flat: triangle • square • pentagon • hexagon • octagon • decagon
Curved: circle
Retrieved from "http://hi.gher.space/wiki/Pentagon"