A geometric realization without self-intersections does exist for Dyck's regular map

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Abstract

Even in our decade there is still an extensive search for analogues of the Platonic solids. In a recent paper Schulte and Wills [13] discussed properties of Dyck's regular map of genus 3 and gave polyhedral realizations for it allowing self-intersections. This paper disproves their conjecture in showing that there is a geometric polyhedral realization (without self-intersections) of Dyck's regular map {3, 8}6 already in Euclidean 3-space. We describe the shape of this new regular polyhedron. © 1989 Springer-Verlag New York Inc.

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APA

Bokowski, J. (1989). A geometric realization without self-intersections does exist for Dyck’s regular map. Discrete & Computational Geometry, 4(1), 583–589. https://doi.org/10.1007/BF02187748

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