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Zeitschrift für Kristallographie - Crystalline Materials

Editor-in-Chief: Pöttgen, Rainer

Ed. by Antipov, Evgeny / Bismayer, Ulrich / Boldyreva, Elena V. / Friese, Karen / Huppertz, Hubert / Tiekink, E. R. T.

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Volume 123, Issue 6


On densest packings of ellipsoids1

Takeo Matsumoto / Werner Nowacki
Published Online: 2010-07-28 | DOI: https://doi.org/10.1524/zkri.1966.123.6.401


Assuming that the densest packings of ellipses or ellipsoids are only those which result from the closest packings of circles or spheres respectively by an affine transformation, 2 different densest packings of ellipses and 13 different densest packings of ellipsoids are derived: Two packings of ellipses (C2vIV and C2I), seven packings of ellipsoids (D4h17, D3d5, D2h23, D2h25, two × C2h3, Ci1) and six packings of ellipsoids (D6h4, D2h17, C2h2, C2h3, C2h6, Ci1). They are related to the closest packing of circles (C6vI), the c.c.p. of spheres (Oh5) and the h.c.p. of spheres (D6h4) respectively. These densest packings of ellipses and ellipsoids (which are parallel arrangements) have the following characteristics:

  1. they have the same density as the corresponding circle and sphere packing (s) (ϱ = [unk] = 0.9069… in the plane and ϱ = [unk] = 0.7404… in space);

  2. they have the same number of contacts as the corresponding circle and sphere packing(s): 6 resp. 12;

  3. their space groups are subgroups of tho corresponding circle and sphere packings (C6vI resp. Oh5 and D6h4), with the same centers of symmetry.

About the article

Published Online: 2010-07-28

Published in Print: 1966-12-01

Citation Information: Zeitschrift für Kristallographie, Volume 123, Issue 6, Pages 401–421, ISSN (Online) 0044-2968, ISSN (Print) 1433-7266, DOI: https://doi.org/10.1524/zkri.1966.123.6.401.

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