Pyroteron (EntityTopic, 17)
From Hi.gher. Space
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- | {{Shape| | + | <[#ontology [kind topic] [cats 5D Simplex]]> |
- | + | {{STS Shape | |
- | + | | dim=5 | |
+ | | elements=6, 15, 20, 15, 6 | ||
+ | | genus=0 | ||
+ | | 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} | ||
+ | | vlayout=(([[Triangle|3]][[Tetrahedron|<sup>3</sup>]])<sup>[[Pentachoron|4]]</sup>)<sup>5</sup> | ||
+ | | vfigure=[[Pentachoron]], edge 1 | ||
+ | | 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]]. | ||
== Equations == | == Equations == | ||
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<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}} |
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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 |