Polytopal approximation of elongated convex bodies
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Gilles Bonnet
Abstract
This paper presents bounds for the best approximation, with respect to the Hausdorff metric, of a convex body K by a circumscribed polytope P with a given number of facets. These bounds are of particular interest if K is elongated. To measure the elongation of the convex set, its isoperimetric ratio Vj(K)1/jVi(K)−1/i is used.
Acknowledgements
The author gratefully acknowledges Matthias Reitzner, Christoph Thäle, Martin Henk and the referee for their many helpful suggestions.
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Articles in the same Issue
- Frontmatter
- The non-solvable doubly transitive dimensional dual hyperovals
- On the real differential of a slice regular function
- Generalized null 2-type immersions in Euclidean space
- A dual rigidity of the sphere and the hyperbolic plane
- The conjugacy locus of Cayley–Salmon lines
- Steiner’s Porism in finite Miquelian Möbius planes
- Enumeration of complex and real surfaces via tropical geometry
- On complete Yamabe solitons
- Polytopal approximation of elongated convex bodies
- A note on commutative semifield planes
- Quartic surfaces with icosahedral symmetry
Articles in the same Issue
- Frontmatter
- The non-solvable doubly transitive dimensional dual hyperovals
- On the real differential of a slice regular function
- Generalized null 2-type immersions in Euclidean space
- A dual rigidity of the sphere and the hyperbolic plane
- The conjugacy locus of Cayley–Salmon lines
- Steiner’s Porism in finite Miquelian Möbius planes
- Enumeration of complex and real surfaces via tropical geometry
- On complete Yamabe solitons
- Polytopal approximation of elongated convex bodies
- A note on commutative semifield planes
- Quartic surfaces with icosahedral symmetry
