Abstract
We prove the analogue of Eberhard’s Theorem for symmetric convex 3-polytopes with a 4-valent graph, and disprove a conjecture of the late T. Motzkin about realizing symmetric convex 3-polytopes so that all of their geodesics are in planes.
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This research was supported by the National Research Council of Canada Grant A-3999.
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Zaks, J. On realizing symmetric 3-polytopes. Israel J. Math. 10, 244–251 (1971). https://doi.org/10.1007/BF02771576
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DOI: https://doi.org/10.1007/BF02771576