A New Lower Bound on Translative Covering Density of Tetrahedra

We improve the lower bound on the translative covering density of tetrahedra found by Y. Li, M. Fu and Y. Zhang. Our method improves the bound from 1.00122 to 1.0075, but also shows the existence of similar lower density bounds for any polyhedron which has a face without opposite parallel face or edge.

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Publication Details

Journal
Studia Scientiarum Mathematicarum Hungarica
Published
2024-10-11
DOI
https://doi.org/10.1556/012.2024.04316
Primary Topic
Computational Geometry and Mesh Generation
Type
article
Field-Weighted Citation Impact
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article

A New Lower Bound on Translative Covering Density of Tetrahedra

András Bezdek
Studia Scientiarum Mathematicarum Hungarica
Computational Geometry and Mesh Generation
article

A New Lower Bound on Translative Covering Density of Tetrahedra

András Bezdek
article en

Abstract

We improve the lower bound on the translative covering density of tetrahedra found by Y. Li, M. Fu and Y. Zhang. Our method improves the bound from 1.00122 to 1.0075, but also shows the existence of similar lower density bounds for any polyhedron which has a face without opposite parallel face or edge.

Studia Scientiarum Mathematicarum HungaricaVol. 61(3)
HUN-REN Alfréd Rényi Institute of Mathematics (HU), Parker University (US), Auburn University (US)
Openalex Percentile: Top 65%
Computational Geometry and Mesh Generation
DOISourceOpenAlex
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