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A279022
Greatest possible number of diagonals of a polyhedron having n edges.
5
0, 1, 1, 2, 4, 5, 7, 10, 13, 16, 20, 23, 28, 34, 37, 44, 52, 55, 64, 73, 77, 88, 100, 103, 115, 128, 133
OFFSET
8,4
COMMENTS
Note that a polyhedron with 6 edges (a tetrahedron) has no diagonals and a polyhedron having exactly 7 edges does not exist.
If n = 3k where k > 3 than the maximum number of diagonals is achieved by a simple polyhedron with k+2 faces.
According to the Grünbaum-Motzkin Theorem a(3k) = 2*k^2-13*k+30, for all k>11.
Additionally for all k>11 a(3k+1) <= 2*k^2-13*k+36 and a(3k+2) <= 2*k^2-11*k+27.
REFERENCES
1. B. Grünbaum, Convex Polytopes, 2nd edition, Springer, 2003.
LINKS
B. Grünbaum, T. S. Motzkin, The number of hexagons and the simplicity of geodesics of certain polyhedra , Canadian journal of Mathematics, 15 (1963), pp. 744-751.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Vladimir Letsko, Dec 03 2016
STATUS
approved