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An isoperimetric
problem for three-dimensional parallelohedra
Zsolt Lángi |
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Vol. 316 (2022), No. 1, 169–181
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Abstract |
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The aim of this note is to investigate isoperimetric-type problems for -dimensional parallelohedra; that is, for convex polyhedra whose translates tile the -dimensional Euclidean space. Our main result states that among -dimensional parallelohedra with unit volume, the one with minimal mean width is the regular truncated octahedron. |
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Keywords
parallelohedra, zonotopes, discrete isoperimetric problems,
tiling, Kepler's conjecture, honeycomb conjecture, Kelvin's
conjecture
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Mathematical Subject Classification
Primary: 52B60
Secondary: 52A40, 52C22
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Milestones
Received: 24 February 2021
Revised: 7 October 2021
Accepted: 5 November 2021
Published: 26 February 2022
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Authors |
| Zsolt Lángi | |
| Morphodynamics Research Group and
Department of Geometry Budapest University of Technology Budapest Hungary |
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