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Are Denser Packings of Spheres than Closest Packings Possible? How Many Closest Packings of Spheres Exist?
Author(s) -
Müller Ulrich
Publication year - 1992
Publication title -
angewandte chemie international edition in english
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.831
H-Index - 550
eISSN - 1521-3773
pISSN - 0570-0833
DOI - 10.1002/anie.199207271
Subject(s) - spheres , polyhedron , circle packing , intuition , snowflake , sphere packing , physics , mathematics , combinatorics , geometry , philosophy , epistemology , astronomy , meteorology , snow
“On the six‐cornered snowflake” is the title of a short work by Johannes Kepler from 1611, in which an arrangement of spheres that is known today as cubic closest packing was first described. The modern term is based on the intuition of whole generations of chemists, physicists, and crystallographers. A rigorous mathematical proof that the maximum space‐filling is really achieved in this packing was provided in 1991 by W. Y. Hsiang. Central to his proof are the domains of influence of the spheres, which can be described by surrounding polyhedrons and which must completely fill the space.