In five-dimensional geometry , a demipenteract or 5-demicube is a semiregular 5-polytope , constructed from a 5-hypercube ( penteract ) with alternated vertices removed.
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78-573: A semiregular polytope, labeling it as HM 5 for a 5-dimensional half measure polytope. Coxeter named this polytope as 1 21 from its Coxeter diagram , which has branches of length 2, 1 and 1 with a ringed node on one of the short branches, [REDACTED] [REDACTED] [REDACTED] [REDACTED] [REDACTED] [REDACTED] [REDACTED] and Schläfli symbol { 3 3 , 3 3 } {\displaystyle \left\{3{\begin{array}{l}3,3\\3\end{array}}\right\}} or {3,3 }. It exists in
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104-491: Is different from Wikidata All article disambiguation pages All disambiguation pages e5">e5 The requested page title contains unsupported characters : ">". Return to Main Page . E5 polytope It was discovered by Thorold Gosset . Since it was the only semiregular 5-polytope (made of more than one type of regular facets ), he called it a 5-ic semi-regular . E. L. Elte identified it in 1912 as
117-557: The Wythoff construction , dividing the full group order of a subgroup order by removing one mirror at a time. * = The number of elements (diagonal values) can be computed by the symmetry order D 5 divided by the symmetry order of the subgroup with selected mirrors removed. It is a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family. There are 23 Uniform 5-polytopes (uniform 5-polytopes) that can be constructed from
130-532: The k 21 polytope family as 1 21 with the Gosset polytopes: 2 21 , 3 21 , and 4 21 . The graph formed by the vertices and edges of the demipenteract is sometimes called the Clebsch graph , though that name sometimes refers to the folded cube graph of order five instead. Cartesian coordinates for the vertices of a demipenteract centered at the origin and edge length 2 √ 2 are alternate halves of
143-417: The penteract : with an odd number of plus signs. This configuration matrix represents the 5-demicube. The rows and columns correspond to vertices, edges, faces, cells and 4-faces. The diagonal numbers say how many of each element occur in the whole 5-demicube. The nondiagonal numbers say how many of the column's element occur in or at the row's element. The diagonal f-vector numbers are derived through
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#1732844955438156-477: The D 5 symmetry of the demipenteract, 8 of which are unique to this family, and 15 are shared within the penteractic family. The 5-demicube is third in a dimensional series of semiregular polytopes . Each progressive uniform polytope is constructed vertex figure of the previous polytope. Thorold Gosset identified this series in 1900 as containing all regular polytope facets, containing all simplexes and orthoplexes ( 5-simplices and 5-orthoplexes in
169-447: The same term This disambiguation page lists articles associated with the same title formed as a letter–number combination. If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=E5&oldid=1246019285 " Category : Letter–number combination disambiguation pages Hidden categories: Short description
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