✦ LIBER ✦

SEMIREGULAR POLYHEDRA

✍ Scribed by Rick N. Blake and Charles Verhille

Book ID: 127070037
Publisher: National Council of Teachers of Mathematics
Year: 1982
Weight: 757 KB
Volume: 75
Category: Article
ISSN: 0025-5769
DOI: 10.2307/27963090

No coin nor oath required. For personal study only.

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On the sphericity of the graphs of semir

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The sphericity of a graph G is the smallest integer n such that G can be represented as the intersection graph of a family of unit-diameter spheres in Euclidean n-space E n. We determine here the sphericities of the graph of semiregular polyhedra in E 3 except a few prisms.

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In doing so he also gave a full description of those finite groups which have a Ž . Ž . representation D over ‫ރ‬ such that D g has no eigenvalue 1 for any nontrivial element g g G. In our terminology such a group is called w x Ž . semiregular. One of the results in 17 characterizes SL 5 as the only

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