Icosahedral truncate (EntityTopic, 11)

From Hi.gher. Space

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{{Shape
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{{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
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| schlaefli=t{[[Pentagon|3,]]5}
 
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| 20=SSC
 
| ssc={G5<sup>3</sup>}X6
| ssc={G5<sup>3</sup>}X6
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| extra={{STS Uniform polytope
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| 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>
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| kana=イコト
| kana=イコト
| dual=[[Pentakis dodecahedron]]
| dual=[[Pentakis dodecahedron]]
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}}
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}}}}
== Geometry ==
== Geometry ==

Revision as of 15:12, 14 March 2008


Geometry

Equations

  • Variables:
l ⇒ length of edges of the truncated icosahedron
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: tetrahedroncubeoctahedrondodecahedronicosahedron
Direct truncates: tetrahedral truncatecubic truncateoctahedral truncatedodecahedral truncateicosahedral truncate
Mesotruncates: stauromesohedronstauroperihedronstauropantohedronrhodomesohedronrhodoperihedronrhodopantohedron
Snubs: snub staurohedronsnub rhodohedron
Curved: spheretoruscylinderconefrustumcrind