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Ghost symmetry and an analogue of Steinitz’s theorem

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Abstract

A ghost symmetry of a point configuration is a symmetry which appears in one or more of its projections. Generally, ghost symmetries are more interesting when they are abundant. Presented here is a necessary and sufficient condition for a list of three involutions to correspond to a point configuration whose ghost symmetries realize those involutions. Associated with any such triple of involutions is a Tait-colored graph, and the characterization is essentially 3-connectedness. The main theorem therefore appears to be a close analogue of the classical characterization of edge graphs of 3-dimensional convex polytopes due to Steinitz.

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Authors and Affiliations

  1. Department of Mathematics, MS 5248, Western Michigan University, Kalamazoo, MI, 49008-5248, USA

    David A. Richter

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  1. David A. Richter
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Correspondence to David A. Richter.

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Richter, D.A. Ghost symmetry and an analogue of Steinitz’s theorem. Beitr Algebra Geom 52, 205–219 (2011). https://doi.org/10.1007/s13366-011-0012-3

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  • DOI: https://doi.org/10.1007/s13366-011-0012-3

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