Pyroteron (EntityTopic, 17)
From Hi.gher. Space
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| - | {{Shape | + | {{STS Shape |
| - | + | ||
| name=Hexateron | | name=Hexateron | ||
| dim=5 | | dim=5 | ||
| elements=6, ?, ?, ?, 6 | | elements=6, ?, ?, ?, 6 | ||
| genus=0 | | genus=0 | ||
| - | |||
| ssc=xPPPP | | ssc=xPPPP | ||
| - | | | + | | extra={{STS Rotope |
| - | | | + | | attrib=pure |
| + | | notation=1<sup>4</sup> x<sup>yzwφ</sup> | ||
| + | | index=89 | ||
| + | }}{{STS Uniform polytope | ||
| schlaefli={[[Triangle|3,]][[Tetrahedron|3,]][[Pentachoron|3,]]3} | | schlaefli={[[Triangle|3,]][[Tetrahedron|3,]][[Pentachoron|3,]]3} | ||
| vlayout=(([[Triangle|3]][[Tetrahedron|<sup>3</sup>]])<sup>[[Pentachoron|4]]</sup>)<sup>5</sup> | | vlayout=(([[Triangle|3]][[Tetrahedron|<sup>3</sup>]])<sup>[[Pentachoron|4]]</sup>)<sup>5</sup> | ||
| vfigure=[[Pentachoron]], edge 1 | | vfigure=[[Pentachoron]], edge 1 | ||
| dual=''Self-dual'' | | dual=''Self-dual'' | ||
| - | }} | + | }}}} |
The '''hexateron''' is the 5-dimensional [[simplex]]. It is a special case of the [[pyramid]] where the base is a [[pentachoron]]. | The '''hexateron''' is the 5-dimensional [[simplex]]. It is a special case of the [[pyramid]] where the base is a [[pentachoron]]. | ||
Revision as of 15:10, 14 March 2008
The hexateron is the 5-dimensional simplex. It is a special case of the pyramid where the base is a pentachoron.
Equations
- Variables:
l ⇒ length of the edges of the hexateron
- All points (x, y, z, w, φ) that lie on the surface of a hexateron will satisfy the following equation:
Unknown
- The hypervolumes of a hexateron are given by:
Unknown
- The flunic cross-sections (n) of a hexateron are:
Unknown
| Notable Pentashapes | |
| Flat: | pyroteron • aeroteron • geoteron |
| Curved: | tritorus • pentasphere • glone • cylspherinder • tesserinder |
