Aeroteron (EntityTopic, 14)
From Hi.gher. Space
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| - | {{Shape | + | {{STS Shape |
| name=Icosidodecateron | | name=Icosidodecateron | ||
| dim=5 | | dim=5 | ||
| elements=32, 80, 80, 40, 10 | | elements=32, 80, 80, 40, 10 | ||
| genus=0 | | genus=0 | ||
| - | |||
| ssc=<nowiki>{{{</nowiki>G3<sup>3</sup>}<sup>4</sup>}<sup>8</sup>} | | ssc=<nowiki>{{{</nowiki>G3<sup>3</sup>}<sup>4</sup>}<sup>8</sup>} | ||
| - | | | + | | extra={{STS Rotope |
| + | | index=99 | ||
| + | }}{{STS Uniform polytope | ||
| schlaefli={[[Triangle|3]],[[Tetrahedron|3]],[[Pentachoron|3]],4} | | schlaefli={[[Triangle|3]],[[Tetrahedron|3]],[[Pentachoron|3]],4} | ||
| vlayout=(([[Triangle|3]]<sup>[[Tetrahedron|3]]</sup>)<sup>[[Pentachoron|4]]</sup>)<sup>8</sup> | | vlayout=(([[Triangle|3]]<sup>[[Tetrahedron|3]]</sup>)<sup>[[Pentachoron|4]]</sup>)<sup>8</sup> | ||
| vfigure=[[Hexadecachoron]] | | vfigure=[[Hexadecachoron]] | ||
| dual=[[Pentacube]] | | dual=[[Pentacube]] | ||
| - | }} | + | }}}} |
The '''icosidodecateron''' is the 5-dimensional [[cross polytope]], and the [[dual]] of the [[pentacube]]. | The '''icosidodecateron''' is the 5-dimensional [[cross polytope]], and the [[dual]] of the [[pentacube]]. | ||
Revision as of 14:36, 14 March 2008
The icosidodecateron is the 5-dimensional cross polytope, and the dual of the pentacube.
Geometry
Equations
- Variables:
l ⇒ length of the edges of the icosidodecateron
- All points (x, y, z, w, φ) that lie on the surteron of a pentacube will satisfy the following equation:
Unknown
- The hypervolumes of an icosidodecateron are given by:
Unknown
- The flunic cross-sections (n) of a n icosidodecateron are:
Unknown
| Notable Pentashapes | |
| Flat: | pyroteron • aeroteron • geoteron |
| Curved: | tritorus • pentasphere • glone • cylspherinder • tesserinder |
| 98. <[xy]zwφ> Wide icosidodecateron | 99. <xyzwφ> Icosidodecateron | 100. <(xy)zwφ> Tribicone |
| List of bracketopes | ||
