Hexeract

A hexeract is a name for a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 penteract 5-faces.

The name "hexeract" is derived from combining the name tesseract (the "4-cube") with "hex" for six (dimensions) in Greek.

It can also be called a regular dodeca-6-tope or dodecapeton, being made of 12 regular facets.

It is a part of an infinite family of polytopes, called hypercubes. The dual of a penteract can be called a hexacross, and is a part of the infinite family of cross-polytopes.

Applying an "alternation" operation, deleting alternating vertices of the hexeract, creates another uniform polytope, called a demihexeract, (part of an infinite family called demihypercubes), which has 12 demipenteractic and 32 hexateronic facets.

Cartesian coordinates

Cartesian coordinates for the vertices of a hexeract centered at the origin and edge length 2 are: (±1,±1,±1,±1,±1,±1)while the interior of the same consists of all points (x₀, x₁, x₂, x₃, x₄, x₅) with -1 < x_i < 1.

Projections

See also

* Other Regular 6-polytopes:
** Heptapeton (6-simplex) - {3,3,3,3,3}
** Hexacross (6-Cross polytope) - {3,3,3,3,4}
* Others in the Hypercubes family
**Square - {4}
**Cube - {4,3}
**Tesseract - {4,3,3}
**Penteract - {4,3,3,3}
**"Hexeract" - {4,3,3,3,3}
**Hepteract - {4,3,3,3,3,3}
**Octeract - {4,3,3,3,3,3,3}
**Enneract - {4,3,3,3,3,3,3,3}
**10-cube - {4,3,3,3,3,3,3,3,3}
**...

References

* Coxeter, H.S.M. "Regular Polytopes", (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8 p.296, Table I (iii): Regular Polytopes, three regular polytopes in n-dimensions (n>=5)

External links

*
*GlossaryForHyperspace | anchor=Measure | title=Measure polytope
* [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary: hypercube] Garrett Jones