Geodesic
The Radii of Polyhedrons
Canadian journal of mathematics, Tome 35 (1983) no. 1, pp. 33-42

Voir la notice de l'article provenant de la source Cambridge University Press

1. Introduction. Let P be a polyhedron (i.e., a 3-dimensional polytope). A path in P is defined as a sequence of edges (x 1, x 2), ..., (x i−1, x i), (x i , x i−1), ..., (x n−1, xn ) where (xi , x i+1) denotes the edge with endpoints Xi and X i+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. 
Enns, T. C. The Radii of Polyhedrons. Canadian journal of mathematics, Tome 35 (1983) no. 1, pp. 33-42. doi: 10.4153/CJM-1983-002-3
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