Hepteract

A hepteract is a seven-dimensional hypercube with 128 vertices, 448 edges, 672 square faces, 560 cubic cells, 280 tesseract 4-faces, 84 penteract 5-faces, and 14 hexeract 6-faces.

The name "hepteract" is derived from combining the name tesseract (the "4-cube") with "hepta" for seven (dimensions) in Greek.

It can also be called a regular tetradeca-7-tope or tetradecaexon, being made of 14 regular facets.

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

Applying an "alternation" operation, deleting alternating vertices of the hepteract, creates another uniform polytope, called a demihepteract, (part of an infinite family called demihypercubes), which has 14 demihexeractic and 64 heptaexonic 6-faces.

Cartesian coordinates

Cartesian coordinates for the vertices of a hepteract centered at the origin and edge length 2 are: (±1,±1,±1,±1,±1,±1,±1)while the interior of the same consists of all points (x₀, x₁, x₂, x₃, x₄, x₅, x₆) with -1 < x_i < 1.

Projections

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