Geodesics on regular polyhedra with endpoints at the vertices

DOI10.1007/s40598-016-0040-zzbMath1432.53058OpenAlexW2334292086MaRDI QIDQ726611

Dmitry Fuchs

Publication date: 12 July 2016

Published in: Arnold Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40598-016-0040-z

zbMATH Keywords

endpointsregular polyhedrageodesic segments

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Geodesics in global differential geometry (53C22)

Related Items (7)

Vertex to Vertex Geodesics on Platonic Solids ⋮ Geodesics on the regular tetrahedron and the cube ⋮ Simple Closed Geodesics on Regular Tetrahedra in Spaces of Constant Curvature ⋮ Shortest Paths on Cubes ⋮ Billiard trajectories in regular polygons and geodesics on regular polyhedra ⋮ A Trajectory from a Vertex to Itself on the Dodecahedron ⋮ Platonic Solids and High Genus Covers of Lattice Surfaces

Cites Work

• Periodic billiard trajectories in regular polygons and closed geodesics on regular polyhedra
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