Aeroteron (EntityTopic, 14)

From Higher Dimensions Database

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
Unknown
Unknown

Incidence matrix

Dual: geoteron

#TXIDVaEa3aC1aH4.1aTypeName
0 Va = point ;
1 Ea 2 = digon ;
2 3a 33 = triangle ;
3 C1a 464 = tetrahedron ;
4 H4.1a 510105 = pyrochoron ;
5 H5.1a 1040808032 = aeroteron ;

Usage as facets

This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.


Cross polytopes
diamondoctahedronaerochoronaeroteronaeropeton


Notable Pentashapes
Flat: pyroteronaeroterongeoteron
Curved: tritoruspentasphereglonecylspherindertesserinder


31. [IIIII]
Geoteron
32. <IIIII>
Aeroteron
33. (IIIII)
Pentasphere
List of bracketopes