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A Generation Procedure for the Simple 3-Polytopes With Cyclically 5-Connected Graphs

Published online by Cambridge University Press:  20 November 2018

Jean W. Butler
Jean W. Butler*
Affiliation:
McGill University, Montreal, Quebec
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In this paper we derive a generation procedure for the simple (3-valent) 3-polytopes with cyclically 5-connected graphs. (A graph is called cyclically n-connected if it cannot be broken into two components, each containing a cycle, by the removal of fewer than n edges.) We define three new types of face splitting and we show, in Theorems 16 and 17, that the simple 3-polytopes with cyclically 5-connected graphs are exactly the polytopes obtained from the dodecahedron by these face splittings.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 3 , June 1974 , pp. 686 - 708
Copyright
Copyright © Canadian Mathematical Society 1974

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