Abstract
In a remarkable paper [4] Grünbaum and Shephard stated that there is no polyhedron of genusg>0, such that its symmetry group acts transitively on its faces. If this condition is slightly weakened, one obtains some interesting polyhedra with face-transitivity (resp. vertex-transitivity).
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Wills, J.M. On polyhedra with transitivity properties. Discrete Comput Geom 1, 195–199 (1986). https://doi.org/10.1007/BF02187694
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DOI: https://doi.org/10.1007/BF02187694