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On Polyhedral Realizability of Certain Sequences

Published online by Cambridge University Press:  20 November 2018

E. Jucovič
E. Jucovič*
Affiliation:
Prírodovedecká fakulta Šafárikovej University, KošiceCzechoslovakia
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A finite sequence (pk) = (p3, p4,…) of non-negative integers shall be called realizable provided there exists a 3-valent 3-polytope P which has pi. i-gonal faces for every i. P is called a realization of (pk).

For realizability of a sequence (pk), from Euler's formula follows

(*) as a necessary condition.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 1 , February 1969 , pp. 31 - 39
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Brückner, M., Vielecke und Vielflache. (Leipzig, 1900).Google Scholar
2. Grünbaum, B. and Motzkin, T. S., The number of hexagons and the simplicity of geodesies on certain polyhedra. Canad. J. Math. 15 (1963) 744–751.Google Scholar
3. Grünbaum, B., Convex Polytopes. (J, Wiley, 1967).Google Scholar
4. Grünbaum, B., A companion to Eberhard′s Theorem (preprint).Google Scholar