Title :
Random exploration of the three regular polytopes
Author :
Blachman, Nelson M.
Author_Institution :
GTE Gov. Syst. Corp., Mountain View, CA, USA
fDate :
11/1/1995 12:00:00 AM
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;
Journal_Title :
Information Theory, IEEE Transactions on
