Aeroteron (EntityTopic, 14)
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| + | <[#ontology [kind topic] [cats 5D Cross_polytope]]> | ||
| + | {{STS Shape | ||
| + | | dim=5 | ||
| + | | elements=32, 80, 80, 40, 10 | ||
| + | | genus=0 | ||
| + | | ssc=<xyzwφ> | ||
| + | | ssc2=K5c16 | ||
| + | | extra={{STS Bracketope | ||
| + | | index=32 | ||
| + | }}{{STS Uniform polytope | ||
| + | | schlaefli={[[Triangle|3]],[[Tetrahedron|3]],[[Pentachoron|3]],4} | ||
| + | | vlayout=(([[Triangle|3]]<sup>[[Tetrahedron|3]]</sup>)<sup>[[Pentachoron|4]]</sup>)<sup>8</sup> | ||
| + | | vfigure=[[Hexadecachoron]] | ||
| + | | dual=[[Pentacube]] | ||
| + | }}}} | ||
| + | The '''aeroteron''', also known as the '''icosidodecateron''', the '''triacontaditeron''' and the '''pentacross''', is the five-dimensional [[cross polytope]], and is the [[dual]] of the [[geoteron]]. | ||
| + | == Equations == | ||
| + | *Variables: | ||
| + | <blockquote>''l'' ⇒ length of the edges of the icosidodecateron</blockquote> | ||
| + | |||
| + | *All points (''x'', ''y'', ''z'', ''w'', ''φ'') that lie on the [[surteron]] of a pentacube will satisfy the following equation: | ||
| + | <blockquote>''Unknown''</blockquote> | ||
| + | |||
| + | *The [[hypervolume]]s of an icosidodecateron are given by: | ||
| + | <blockquote>''Unknown''</blockquote> | ||
| + | |||
| + | *The [[flunic]] [[cross-section]]s (''n'') of a n icosidodecateron are: | ||
| + | <blockquote>''Unknown''</blockquote> | ||
| + | |||
| + | <[#polytope [id 91]]> | ||
| + | |||
| + | {{Cross polytopes|5}} | ||
| + | {{Pentashapes}} | ||
| + | {{Bracketope Nav|31|32|33|[IIIII]<br>Geoteron|<nowiki><IIIII></nowiki><br>Aeroteron|(IIIII)<br>Pentasphere|tera}} | ||
Latest revision as of 21:14, 14 March 2014
The aeroteron, also known as the icosidodecateron, the triacontaditeron and the pentacross, is the five-dimensional cross polytope, and is the dual of the geoteron.
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
Incidence matrix
Dual: geoteron
| # | 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 | = pyrochoron | ; | |
| 5 | H5.1a | 10 | 40 | 80 | 80 | 32 | = aeroteron | ; |
Usage as facets
This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.
| Cross polytopes |
| diamond • octahedron • aerochoron • aeroteron • aeropeton |
| Notable Pentashapes | |
| Flat: | pyroteron • aeroteron • geoteron |
| Curved: | tritorus • pentasphere • glone • cylspherinder • tesserinder |
| 31. [IIIII] Geoteron | 32. <IIIII> Aeroteron | 33. (IIIII) Pentasphere |
| List of bracketopes | ||
