Enneract

An enneract is a nine-dimensional hypercube with 512 vertices, 2304 edges, 4608 square faces, 5376 cubic cells, 4032 tesseract 4-faces, 2016 penteract 5-faces, 672 hexeract 6-faces, 144 hepteract 7-faces, and 18 octeract 8-faces.

The name "enneract" is derived from combining the name tesseract (the "4-cube") with "enne" for nine (dimensions) in Greek.

It can also be called a regular octadeca-9-tope or octadecayotton, being made of 18 regular facets.

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

Cartesian coordinates

Cartesian coordinates for the vertices of an enneract centered at the origin and edge length 2 are: (±1,±1,±1,±1,±1,±1,±1,±1,±1)while the interior of the same consists of all points ("x"₀, "x"₁, "x"₂, "x"₃, "x"₄, "x"₅, "x"₆, "x"₇, "x"₈) with −1 < "x"_"i" < 1.

Projections

Derived polytopes

Applying an "alternation" operation, deleting alternating vertices of the "enneract", creates another uniform polytope, called a "demienneract", (part of an infinite family called demihypercubes), which has 18 demiocteractic and 256 enneazettonic facets.

See also

*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