- Penteract
In five dimensional

geometry , a**penteract**is a name for a five dimensionalhypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10tesseract hypercell s.The name "penteract" is derived from combining the name

tesseract (the "4-cube") with "pente" for five (dimensions) in Greek.It can also be called a regular

**deca-5-tope**or**decateron**, being made of 10 regular facets.It is a part of an infinite family of polytopes, called

hypercube s. The dual of a penteract can be called apentacross , of the infinite family ofcross-polytope s.Applying an "alternation" operation, deleting alternating vertices of the penteract, creates another

uniform polytope , called ademipenteract , which is also part of an infinite family called thedemihypercube s.**Cartesian coordinates**Cartesian coordinates for the vertices of a penteract centered at the origin and edge length 2 are: (±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}) with -1 < x_{i}< 1.**Projections****See also*** Other Regular

5-polytope s:

**5-simplex (hexateron) - {3,3,3,3}

**5-orthoplex (pentacross) - {3,3,3,4}

**5-demicube (demipenteract) - {3^{1,2,1}}

* Others in thehypercube 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

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2010.*

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