The edge-transitive polytopes that are not vertex-transitive
نویسندگان
چکیده
In 3-dimensional Euclidean space there exist two exceptional polyhedra, the rhombic dodecahedron and triacontahedron, only known polytopes (besides polygons) that are edge-transitive without being vertex-transitive. We show these polyhedra do not have higher-dimensional analogues, is, in dimension d ? 4, edge-transitivity of convex implies vertex-transitivity.More generally, we give a classification all which at same time edges length, an edge in-sphere bipartite edge-graph. any such polytope 4 is
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ژورنال
عنوان ژورنال: Ars Mathematica Contemporanea
سال: 2022
ISSN: ['1855-3974', '1855-3966']
DOI: https://doi.org/10.26493/1855-3974.2712.6be