Dodecahedron (EntityTopic, 12)
From Hi.gher. Space
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| - | {{Shape | + | {{STS Shape |
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| name=Dodecahedron | | name=Dodecahedron | ||
| image=http://img129.imageshack.us/img129/2226/dodecahedron8do.png | | image=http://img129.imageshack.us/img129/2226/dodecahedron8do.png | ||
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| elements=12, 30, 20 | | elements=12, 30, 20 | ||
| genus=0 | | genus=0 | ||
| - | |||
| ssc={G5<sup>3</sup>} | | ssc={G5<sup>3</sup>} | ||
| - | | | + | | extra={{STS Uniform polytope |
| wythoff=<nowiki>3 | 2 5 </nowiki> | | wythoff=<nowiki>3 | 2 5 </nowiki> | ||
| schlaefli={[[Pentagon|5,]]3} | | schlaefli={[[Pentagon|5,]]3} | ||
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| kana=ﾄﾞ | | kana=ﾄﾞ | ||
| dual=[[Icosahedron]] | | dual=[[Icosahedron]] | ||
| - | }} | + | }}}} |
== Equations == | == Equations == | ||
Revision as of 14:55, 14 March 2008
Equations
- Assumption: Dodecahedron is centered at the origin.
- Variables:
l ⇒ length of edges of the dodecahedron
- The hypervolumes of a dodecahedron are given by:
total edge length = 30l
surface area = 15l2tan(3π10-1)
volume = 5l3(tan(3π10-1))2(tan(sin-1(2sin(π5-1))-1))2-1
- The planar cross-sections (n) of a dodecahedron are:
Unknown
| Notable Trishapes | |
| Regular: | tetrahedron • cube • octahedron • dodecahedron • icosahedron |
| Direct truncates: | tetrahedral truncate • cubic truncate • octahedral truncate • dodecahedral truncate • icosahedral truncate |
| Mesotruncates: | stauromesohedron • stauroperihedron • stauropantohedron • rhodomesohedron • rhodoperihedron • rhodopantohedron |
| Snubs: | snub staurohedron • snub rhodohedron |
| Curved: | sphere • torus • cylinder • cone • frustum • crind |
