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math.CO2012
The Regular Grunbaum Polyhedron of Genus 5
Gabor Gevay, Egon Schulte, Jorg M. Wills
We discuss a polyhedral embedding of the classical Fricke-Klein regular map of genus 5 in ordinary 3-space. This polyhedron was originally discovered by Grunbaum in 1999, but was…
math.CO2012
Kronecker covers, V-construction, unit-distance graphs and isometric point-circle configurations
Gábor Gévay, Tomaž Pisanski
We call a polytope P of dimension 3 admissible if it has the following two properties: (1) for each vertex of P the set of its first-neighbours is coplanar; (2) all planes determin…