New dense superball packings in three dimensions-Reference-Cited by-同舟云学术

New dense superball packings in three dimensions

Published:2020-10-01 Issue:4 Volume:20 Page:473-482
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

Dostert Maria¹,Vallentin Frank²

Affiliation:

1. EPFL, SB TN , Station 8, 1015 , Lausanne , Switzerland

2. Mathematisches Institut , Universität zu Köln , Weyertal 86–90, 50931 , Köln , Germany

Abstract

Abstract We construct a new family of lattice packings for superballs in three dimensions (unit balls for the

l 3 p

$\begin{array}{} \displaystyle l^p_3 \end{array}$

norm) with p ∈ (1, 1.58]. We conjecture that the family also exists for p ∈ (1.58, log2 3 = 1.5849625…]. Like in the densest lattice packing of regular octahedra, each superball in our family of lattice packings has 14 neighbors.

Funder

National Science Foundation

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2020-0002/pdf

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