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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

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3. Grünbaum, B., Convex Polytopes. (J, Wiley, 1967).Google Scholar
4. Grünbaum, B., A companion to Eberhard′s Theorem (preprint).Google Scholar