A279022 Greatest possible number of diagonals of a polyhedron having n edges.

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

Author

Vladimir Letsko, Dec 03 2016

Keywords

• nonn
• more

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

Cf. A002840, A279015, A279019.