Icosahedral truncate (EntityTopic, 11)
From Hi.gher. Space
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| - | {{Shape|Truncated icosahedron|http://fusion-global.org/share/truncicosa.png|3|32, 90, 60|0|t{[[Pentagon|5,]]3}|''Unknown''|''Unknown''|N/A|Isosceles [[triangle]]|Ti|Pentakis dodecahedron}} | + | {{Shape|Truncated icosahedron|http://fusion-global.org/share/truncicosa.png|3|32, 90, 60|0|t{[[Pentagon|5,]]3}|''Unknown''|''Unknown''|N/A|Isosceles [[triangle]]|Ti|[[Pentakis dodecahedron]]}} |
== Geometry == | == Geometry == | ||
=== Equations === | === Equations === | ||
Revision as of 13:46, 16 September 2007
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 |
