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The Radii of Polyhedrons

Published online by Cambridge University Press:  20 November 2018

T. C. Enns
T. C. Enns*
Affiliation:
San Diego Mesa College, San Diego, California
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1. Introduction. Let P be a polyhedron (i.e., a 3-dimensional polytope). A path in P is defined as a sequence of edges (x1, x2), …, (xi−1, xi), (xi, xi−1), …, (xn−1, xn) where (xi, xi+1) denotes the edge with endpoints Xi and Xi+1. Define the length |A| of a path A to be the number of edges of said path. The distance between any two vertices x and y of P is defined to be the least length of all paths of P between x and y. For the purposes of this paper, if x and y lie on a particular path A, the distance between x and y along A will be defined to be the length of the segment of A between x and y. The radius of P is defined to be the smallest integer r for which there exists a vertex v of P such that the distance from v to any other vertex of P is at most r.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 35 , Issue 1 , 01 February 1983 , pp. 33 - 42
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Jucovic, E. and Moon, J. W., The maximum diameter of a convex polyhedron, Mathematics Magazine (1965), 31–32.Google Scholar