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Twenty Problems on Convex Polyhedra Part II

Published online by Cambridge University Press:  03 November 2016

G. C. Shephard
G. C. Shephard*
Affiliation:
School of Mathematics and Physics, University of East Anglia, Wilberforce Road, Norwich, NOR 88 C
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Extract

Let P be a given convex polyhedron and L any plane. Then if L∩P is not empty it is called a plane section of P. Every plane section of P is either a convex polygon, an edge or a vertex of P.

VI. If a convex polyhedron P has v vertices (v ≥4), does there always exist a plane section of P which is a convex n-gon with n ≥ √ v ?

A more general statement of this problem is to ask whether there exists a constant d (0 < d < 1) such that every convex polyhedron P with v vertices possesses a plane section which is an n-gon with n ≥ vd. Problem VI is then equivalent to asking whether d ≤ ½

Type
Research Article
Information
The Mathematical Gazette , Volume 52 , Issue 382 , December 1968 , pp. 359 - 367
Copyright
Copyright © Mathematical Association 1968

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References

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