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math.MG2026
The maximum volume polytope with nine vertices inscribed in the sphere
Steven Hoehner, Jeff Ledford
A classical problem in convex and discrete geometry asks for the convex polyhedron of greatest volume whose vertices are chosen from the unit sphere . For a prescribe…
math.MG2025
A note concerning frames and geometric inequalities
Jeff Ledford, Kevin Rivera-Ayala, Emma Schroeder
One may associate several frames to a given polytope, such as its collection of vertices, edges, or facet normal vectors. In this note, we use these frames to generate geometric in…
math.MG2024
Steiner symmetrization on the sphere
Bushra Basit, Steven Hoehner, Zsolt Lángi +1
The aim of this paper is to introduce a generalization of Steiner symmetrization in Euclidean space for spherical space, which is the dual of the Steiner symmetrization in hyperbol…