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- W1497019849 abstract "Since Grünbaum 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 Gévay, Schulte, and Wills, we now know that the genus range $$mathfrak {g}ge 2$$ 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 regularly on the vertices. Furthermore, the case of rotational tetrahedral symmetry is settled completely: the unique example is already known." @default.
- W1497019849 created "2016-06-24" @default.
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- W1497019849 date "2016-11-15" @default.
- W1497019849 modified "2023-09-27" @default.
- W1497019849 title "Vertex-Transitive Polyhedra of Higher Genus, I" @default.
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- W1497019849 doi "https://doi.org/10.1007/s00454-016-9828-9" @default.
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