Pyroteron (EntityTopic, 17)

From Hi.gher. Space

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{{Shape|Hexateron|''No image''|5|6, ?, ?, ?, 6|0|{[[Triangle|3,]][[Tetrahedron|3,]][[Pentachoron|3,]]3}|N/A|[[Line (object)|E]][[Triangle|T]][[Tetrahedron|T]][[Pentachoron|T]]T|N/A|[[Pentachoron]], edge 1|N/A|''Self-dual''|89}}
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<[#ontology [kind topic] [cats 5D Simplex]]>
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{{STS Shape
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| dim=5
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| elements=6, 15, 20, 15, 6
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| genus=0
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| ssc=xPPPP
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| ssc2=K5x1
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| extra={{STS Tapertope
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| order=1, 4
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| notation=1<sup>4</sup>
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| index=70
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}}{{STS Uniform polytope
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| schlaefli={[[Triangle|3,]][[Tetrahedron|3,]][[Pentachoron|3,]]3}
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| vlayout=(([[Triangle|3]][[Tetrahedron|<sup>3</sup>]])<sup>[[Pentachoron|4]]</sup>)<sup>5</sup>
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| vfigure=[[Pentachoron]], edge 1
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| dual=''Self-dual''
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}}}}
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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]].
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The '''hexateron''' is the 5-dimensional [[simplex]].
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== Equations ==
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== Geometry ==
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A '''hexateron''' is a special case of the [[pyramid]] where the base is a [[pentachoron]].
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=== Equations ===
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*Variables:
*Variables:
<blockquote>''l'' ⇒ length of the edges of the hexateron</blockquote>
<blockquote>''l'' ⇒ length of the edges of the hexateron</blockquote>
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<blockquote>''Unknown''</blockquote>
<blockquote>''Unknown''</blockquote>
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{{Polytera}}
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<[#polytope [id 92]]>
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{{Rotope Nav|88|89|90|<nowiki>I'''I</nowiki><br>Pentachoric prism|<nowiki>I''''</nowiki><br>Hexateron|<nowiki>(I'''I)</nowiki><br>Pentachoric torus}}
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{{Simplices|5}}
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{{Pentashapes}}
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{{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
Unknown
Unknown

Incidence matrix

Dual: Self-dual

#TXIDVaEa3aC1aH4.1aTypeName
0 Va = point ;
1 Ea 2 = digon ;
2 3a 33 = triangle ;
3 C1a 464 = tetrahedron ;
4 H4.1a 510105 = base of pyramid: pyrochoron ;
5 H5.1a 61520156 = 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
Retrieved from "http://hi.gher.space/wiki/Pyroteron"