Pyroteron (EntityTopic, 17)

From Higher Dimensions Database

(Redirected from Hexateron)

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
triangletetrahedronpyrochoronpyroteronpyropeton


Notable Pentashapes
Flat: pyroteronaeroterongeoteron
Curved: tritoruspentasphereglonecylspherindertesserinder


69. [111]2
Triangular prismic dipyramid
70. 14
Hexateron
71. 2111
Contrianglinder
List of tapertopes