Dodecahedron (EntityTopic, 12)
From Hi.gher. Space
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*The [[hypervolume]]s of a dodecahedron are given by: | *The [[hypervolume]]s of a dodecahedron are given by: | ||
<blockquote>total edge length = 30''l''<br> | <blockquote>total edge length = 30''l''<br> | ||
| - | surface area = | + | surface area = 3√(25 + 10√5) {{DotHV}}<br> |
| - | volume = | + | volume = {{Over|(15 + 7√5)|4}} {{DotHV|3}}</blockquote> |
*The [[planar]] [[cross-section]]s (''n'') of a dodecahedron are: | *The [[planar]] [[cross-section]]s (''n'') of a dodecahedron are: | ||
Revision as of 02:04, 18 November 2011
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 = 3√(25 + 10√5) · l2
volume = (15 + 7√5)∕4 · l3
- 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 |
