Icosahedral truncate (EntityTopic, 11)
From Hi.gher. Space
(Difference between revisions)
m |
(update to STS) |
||
Line 1: | Line 1: | ||
- | {{Shape | + | {{STS Shape |
| image=http://fusion-global.org/share/truncicosa.png | | image=http://fusion-global.org/share/truncicosa.png | ||
| dim=3 | | dim=3 | ||
| elements=32, 90, 60 | | elements=32, 90, 60 | ||
| genus=0 | | genus=0 | ||
- | |||
- | |||
| ssc={G5<sup>3</sup>}X6 | | ssc={G5<sup>3</sup>}X6 | ||
+ | | extra={{STS Uniform polytope | ||
+ | | schlaefli=t{[[Pentagon|3,]]5} | ||
| vfigure=Isosceles [[triangle]] | | vfigure=Isosceles [[triangle]] | ||
| vlayout=[[Pentagon|5]]⋅[[Hexagon|6]]<sup>2</sup> | | vlayout=[[Pentagon|5]]⋅[[Hexagon|6]]<sup>2</sup> | ||
Line 12: | Line 12: | ||
| kana=イコト | | kana=イコト | ||
| dual=[[Pentakis dodecahedron]] | | dual=[[Pentakis dodecahedron]] | ||
- | }} | + | }}}} |
== Geometry == | == Geometry == |
Revision as of 15:12, 14 March 2008
Geometry
Equations
- Variables:
l ⇒ length of edges of the truncated icosahedron
- The hypervolumes of a truncated icosahedron are given by:
total edge length = 90l
surface area = 3(32-110+52-1(5+52-12)2-1)l2
volume = (125+52-143)l34-1
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 |