The graphs of polytopes with involutory automorphisms |
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Authors: | David W Barnette |
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Institution: | (1) University of California, Davis, California |
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Abstract: | Steinitz’ theorem states that a graph is the graph of a 3-dimensional convex polytope if and only if it is planar and 3-connected.
Grünbaum has shown that Steinitz’ proof can be modified to characterize the graphs of polytopes that are centrally symmetric
or have a plane of symmetry. We show how to modify Steinitz’ proof to take care of the remaining involutory case—polytopes
that are symmetric about a line.
Research supported by NSF Grant GP-3470. |
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