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- W2953065475 abstract "Since Gruenbaum and Shephard's investigation of self-intersection-free polyhedra with positive genus and vertex-transitive symmetry in 1984 the question of complete classification of such objects in Euclidean 3-space has been open. Due to a recent article by Gevay, Schulte, and Wills, we now know that the genus range g>=2 can only admit a finite number of vertex-transitive polyhedra, all with rotational Platonic symmetry. In this article, we show that the symmetry group must also act simply transitively on the vertices. Furthermore, the case of rotational tetrahedral symmetry is settled completely - the unique example is already known." @default.
- W2953065475 created "2019-06-27" @default.
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- W2953065475 date "2015-02-26" @default.
- W2953065475 modified "2023-09-27" @default.
- W2953065475 title "Vertex-Transitive Polyhedra of Higher Genus, I" @default.
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