Dodecahedron (EntityTopic, 12)
From Hi.gher. Space
(Difference between revisions)
m (fix FLD) |
m |
||
| Line 1: | Line 1: | ||
| + | <[#ontology [kind topic] [cats 3D Regular Polytope]]> | ||
{{STS Shape | {{STS Shape | ||
| name=Dodecahedron | | name=Dodecahedron | ||
| Line 36: | Line 37: | ||
<br clear="all"><br> | <br clear="all"><br> | ||
{{Trishapes}} | {{Trishapes}} | ||
| - | |||
| - | |||
Revision as of 21:56, 12 March 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 = 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 |
