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	On the translative packing densities of tetrahedra and cuboctahedra
	Zong, Chuanming
	2014
关键词	Tetrahedron Cuboctahedron Lattice packing density Translative packing density Hilbert&apos Difference body REGULAR TETRAHEDRA KEPLER CONJECTURE CRYSTALLINE s 18th problem
英文摘要	In 1900, as a part of his 18th problem, Hilbert asked the question to determine the density of the densest tetrahedron packings. However, up to now no mathematician knows the density delta(t)(T) of the densest translative tetrahedron packings and the density delta(c)(T) of the densest congruent tetrahedron packings. This paper presents a local method to estimate the density of the densest translative packings of a general convex solid. As an application, we obtain the upper bound in 0.3673469... <= delta(t)(T) <= 0.3840610 ..., where the lower bound was established by Groemer in 1962, which corrected a mistake of Minkowski. For the density delta(t)(C) of the densest translative cuboctahedron packings, we obtain the upper bound in 0.9183673... <= delta(t)(C) <= 0.9601527... . In both cases we conjecture the lower bounds to be the correct answer. (C) 2014 Elsevier Inc. All rights reserved.; Mathematics; SCI(E); 0; ARTICLE; cmzong@math.pku.edu.cn; 130-190; 260
语种	英语
出处	SCI
出版者	数学进展
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/157322]
专题	数学科学学院
推荐引用方式 GB/T 7714	Zong, Chuanming. On the translative packing densities of tetrahedra and cuboctahedra. 2014-01-01.

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