DocumentCode
1087288
Title
Random exploration of the three regular polytopes
Author
Blachman, Nelson M.
Author_Institution
GTE Gov. Syst. Corp., Mountain View, CA, USA
Volume
41
Issue
6
fYear
1995
fDate
11/1/1995 12:00:00 AM
Firstpage
2081
Lastpage
2087
Abstract
There are just three regular polytopes (the hypercube, cross polytope and the simplex) in Euclidean (n>4) space. We calculate their dimensions, including the distance from the centroid to the periphery in a random direction-that of a white Gaussian-noise vector. As n→∞, this distance becomes very predictable. It differs from the distance near which almost all of the volume and surface of the polytope lie
Keywords
Gaussian noise; hypercube networks; information theory; random processes; signal processing; Euclidean space; centroid; cross polytope; dimensions; distance; hypercube; periphery; random direction; random exploration; regular polytopes; signal subspace; simplex; surface; volume; white Gaussian noise vector; Constellation diagram; Gaussian processes; Geometry; Hypercubes; Information theory;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.476340
Filename
476340
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