Pyroteron (EntityTopic, 17)
From Hi.gher. Space
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| - | {{Shape | + | <[#ontology [kind topic] [cats 5D Simplex]]> |
| - | + | {{STS Shape | |
| - | + | ||
| dim=5 | | dim=5 | ||
| - | | elements=6, | + | | elements=6, 15, 20, 15, 6 |
| genus=0 | | genus=0 | ||
| - | |||
| ssc=xPPPP | | ssc=xPPPP | ||
| - | | | + | | ssc2=K5x1 |
| - | | | + | | extra={{STS Tapertope |
| + | | order=1, 4 | ||
| + | | notation=1<sup>4</sup> | ||
| + | | index=70 | ||
| + | }}{{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 '''pyroteron''', also known as the '''hexateron''', is the five-dimensional [[simplex]]. It is a special case of the [[pyramid]] where the base is a [[pentachoron]]. | |
| - | The '''hexateron''' is the | + | |
== Equations == | == Equations == | ||
| Line 30: | Line 31: | ||
<blockquote>''Unknown''</blockquote> | <blockquote>''Unknown''</blockquote> | ||
| + | <[#polytope [id 92]]> | ||
| + | |||
| + | {{Simplices|5}} | ||
{{Pentashapes}} | {{Pentashapes}} | ||
| - | {{ | + | {{Tapertope Nav|69|70|71|[11<sup>1</sup>]<sup>2</sup><br>Triangular prismic dipyramid|1<sup>4</sup><br>Hexateron|2<sup>1</sup>1<sup>1</sup><br>Contrianglinder|tera}} |
| - | + | ||
Latest revision as of 21:16, 14 March 2014
The pyroteron, also known as the hexateron, is the five-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
Incidence matrix
Dual: Self-dual
| # | TXID | Va | Ea | 3a | C1a | H4.1a | Type | Name |
|---|---|---|---|---|---|---|---|---|
| 0 | Va | = point | ; | |||||
| 1 | Ea | 2 | = digon | ; | ||||
| 2 | 3a | 3 | 3 | = triangle | ; | |||
| 3 | C1a | 4 | 6 | 4 | = tetrahedron | ; | ||
| 4 | H4.1a | 5 | 10 | 10 | 5 | = base of pyramid: pyrochoron | ; | |
| 5 | H5.1a | 6 | 15 | 20 | 15 | 6 | = pyroteron | ; |
Usage as facets
This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.
| Simplices |
| triangle • tetrahedron • pyrochoron • pyroteron • pyropeton |
| Notable Pentashapes | |
| Flat: | pyroteron • aeroteron • geoteron |
| Curved: | tritorus • pentasphere • glone • cylspherinder • tesserinder |
| 69. [111]2 Triangular prismic dipyramid | 70. 14 Hexateron | 71. 2111 Contrianglinder |
| List of tapertopes | ||
