 Eric W. Weisstein, Hypercube at MathWorld.
 Olshevsky, George, Measure polytope at Glossary for Hyperspace.
 Multidimensional Glossary: hypercube Garrett Jones
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Enneract
Vertexedge graph. (*)
Enneract 9cube 


Type  Regular 9polytope 
Family  hypercube 
Schläfli symbol  {4,3,3,3,3,3,3,3} 
CoxeterDynkin diagram  
8faces  18 octeracts 
7faces  144 hepteracts 
6faces  672 hexeracts 
5faces  2016 penteracts 
4faces  4032 tesseracts 
Cells  5376 cubes 
Faces  4608 squares 
Edges  2304 
Vertices  512 
Vertex figure  8simplex 
Symmetry group  B_{9}, [3,3,3,3,3,3,3,4] 
Dual  Enneacross 
Properties  convex 
An enneract is a ninedimensional hypercube with 512 vertices, 2304 edges, 4608 square faces, 5376 cubic cells, 4032 tesseract 4faces, 2016 penteract 5faces, 672 hexeract 6faces, 144 hepteract 7faces, and 18 octeract 8faces.
The name enneract is derived from combining the name tesseract (the 4cube) with enne for nine (dimensions) in Greek.
It can also be called a regular octadeca9tope 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 crosspolytopes.
Cartesian coordinates
Cartesian coordinates for the vertices of a penteract 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 (x0, x1, x2, x3, x4, x5, x6, x7, x8) with −1 < xi < 1.
Projections
An orthogonal projection viewed along the axes of two opposite vertices and the average plane of one edge path between.
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
o square  {4}
o Cube  {4,3}
o Tesseract  {4,3,3}
o Penteract  {4,3,3,3}
o Hexeract  {4,3,3,3,3}
o Hepteract  {4,3,3,3,3,3}
o Octeract  {4,3,3,3,3,3,3}
o ...
References
* Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0486614808 p.296, Table I (iii): Regular Polytopes, three regular polytopes in ndimensions (n>=5)
Links
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
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