Cosmochoron (EntityTopic, 12)
From Hi.gher. Space
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| - | {{Shape | + | {{STS Shape |
| dim=4 | | dim=4 | ||
| elements=120, 720, 1200, 600 | | elements=120, 720, 1200, 600 | ||
| genus=0 | | genus=0 | ||
| - | |||
| ssc=<nowiki>{{</nowiki>G5<sup>3</sup>}<sup>4</sup>} | | ssc=<nowiki>{{</nowiki>G5<sup>3</sup>}<sup>4</sup>} | ||
| + | | extra={{STS Uniform polytope | ||
| schlaefli={[[Pentagon|5,]][[Dodecahedron|3,]]3} | | schlaefli={[[Pentagon|5,]][[Dodecahedron|3,]]3} | ||
| vlayout=([[Pentagon|5]][[Dodecahedron|<sup>3</sup>]])<sup>4</sup> | | vlayout=([[Pentagon|5]][[Dodecahedron|<sup>3</sup>]])<sup>4</sup> | ||
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| kana=ﾍｶ | | kana=ﾍｶ | ||
| dual=[[ｻｺ]] | | dual=[[ｻｺ]] | ||
| - | }} | + | }}}} |
== Geometry == | == Geometry == | ||
Revision as of 14:46, 14 March 2008
Geometry
Equations
- Variables:
l ⇒ length of the edges of the hecatonicosachoron
- All points (x, y, z, w) that lie on the surcell of a hecatonicosachoron will satisfy the following equation:
Unknown
- The hypervolumes of a hecatonicosachoron are given by:
total edge length = 1200l
total surface area = 180l2sqrt(25+10sqrt(5))
surcell volume = 300l3(tan(3π10-1))2(tan(sin-1(2sin(π5-1))-1))
bulk = Unknown
- The realmic cross-sections (n) of a hecatonicosachoron are:
Unknown
| Notable Tetrashapes | |
| Regular: | pyrochoron • aerochoron • geochoron • xylochoron • hydrochoron • cosmochoron |
| Powertopes: | triangular octagoltriate • square octagoltriate • hexagonal octagoltriate • octagonal octagoltriate |
| Circular: | glome • cubinder • duocylinder • spherinder • sphone • cylindrone • dicone • coninder |
| Torii: | tiger • torisphere • spheritorus • torinder • ditorus |
