Steven Hoehner

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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 $S^{2}$ . For a prescribe…

math.MG2026

Dual volume approximation of the Euclidean ball by polytopes with a fixed number of $k$ -faces

Steven Hoehner, Carsten SchÃ¼tt, Elisabeth M. Werner

We study dual volume approximation of the Euclidean ball by polytopes with a prescribed number of $k$ -dimensional faces. This continues the authors' previous work on intrinsic volu…

math.MG2026

From Circles to Convex Bodies: Approximating Curved Shapes by Polytopes

Steven Hoehner

Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects…

math.MG2026

One polytope fits all: Characterization of the Euclidean ball via simultaneous intrinsic volume approximation

Steven Hoehner

We investigate the asymptotic best approximation of a smooth, strictly convex body $K$ in $R^{d}$ by inscribed polytopes with a restricted number of vertices under the intri…

math.MG2025

On the Optimality of Random Partial Sphere Coverings in High Dimensions

Steven Hoehner, Gil Kur

Given $N$ geodesic caps on the unit sphere in $R^{d}$ , whose total normalized surface area is one, what is the maximal proportion of the sphere that their union can cover? I…

math.MG2025

Approximation of the Euclidean ball by polytopes with a fixed number of $k$ -faces

Steven Hoehner, Carsten SchÃ¼tt, Carsten Schütt +1

We derive lower estimates for the approximation of the $d$ -dimensional Euclidean ball by polytopes with a fixed number of $k$ -dimensional faces, $k \in {0, 1, \dots, d - 1}$ . The metri…

The maximum volume polytope with nine vertices inscribed in the sphere

Dual volume approximation of the Euclidean ball by polytopes with a fixed number of k-faces

From Circles to Convex Bodies: Approximating Curved Shapes by Polytopes

One polytope fits all: Characterization of the Euclidean ball via simultaneous intrinsic volume approximation

On the Optimality of Random Partial Sphere Coverings in High Dimensions

Approximation of the Euclidean ball by polytopes with a fixed number of k-faces

Dual volume approximation of the Euclidean ball by polytopes with a fixed number of $k$ -faces

Approximation of the Euclidean ball by polytopes with a fixed number of $k$ -faces