Hexateron

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Regular hexateron 5-simplex
(Orthographic projection)
Type	Regular polyteron
Hypercells	6 {3,3,3}
Cells	15 {3,3}
Faces	20 {3}
Edges	15
Vertices	6
Vertex figure	{3,3,3}
Schläfli symbol	{3,3,3,3}
Coxeter-Dynkin diagram
Dual	Self-dual
Properties	convex

A hexateron is a name for a five dimensional polytope with 6 vertices, 15 edges, 20 triangle faces, 15 tetrahedral cells, 6 5-cell hypercells.

The name hexateron is derived from hexa for six facets in Greek and -teron. It can also be called 5-simplex or hexa-5-tope.

It is a part of an infinite family of self-dual polytopes, called simplexes.

[edit] Cartesian coordinates

The hexateron can be constructed from a pentachoron by adding a 6th vertex such that it is equidistant with all the other vertices of the pentachoron.

For example, the Cartesian coordinates for the vertices of a hexateron (not centered in the origin!), with edge length equal to , may be:

1. 
2. 
3. 
4. 
5. 
6. ;

The xyz orthogonal projection of the first four coordinates corresponds to the coordinates of regular tetrahedron on alternate corners of the cube.

[edit] See also

• Other Regular 5-polytopes:
  • Penteract - {4,3,3,3}
  • Pentacross - {3,3,3,4}
• Others in the simplex family
  • Tetrahedron - {3,3}
  • Pentachoron - {3,3,3}
  • Hexateron - {3,3,3,3}
  • Heptapeton - {3,3,3,3,3}
  • Octaexon - {3,3,3,3,3,3}

[edit] External links

• Glossary for hyperspace
• Polytopes of Various Dimensions
• Multi-dimensional Glossary