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Licensed Unlicensed Requires Authentication Published by De Gruyter (O) November 13, 2015

Density of the p2gg-4c1 packing of ellipses (II)

  • Masaharu Tanemura EMAIL logo and Takeo Matsumoto


As the second paper of the series, the first of which was published in 1997 (M. Tanemura, T. Matsumoto, Density of the p2gg-4c1 packing of ellipses (I). Z. Kristallogr.1997, 212, 637), the p2gg-4c1(b) packing of identical ellipses where four ellipses are included in the rectangular unit cell and where every ellipse has six contacting neighbors, is discussed. It is shown here that the p2gg-4c1(b) packing of ellipses does not exceed the maximum density ρ=π/12 through numerical computations and series expansions. It is also shown that the p2gg-2a2 packing of ellipses has the similar properties and that it is considered as a special case of p2gg-4c1(b) packing. The method of computing the density for every parameter values of aspect ratio and tilt angle is given.

Corresponding author: Masaharu Tanemura, The Institute of Statistical Mathematics, Midori-cho, 10-3, 190-8562 Tachikawa, Japan, E-mail:


The authors thank to the referees for careful reading of our manuscript and for valuable comments. We also thank to Prof. Massimo Nespolo and Prof. Mois Aroyo for their editorial efforts.


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Received: 2015-7-12
Accepted: 2015-10-13
Published Online: 2015-11-13
Published in Print: 2015-12-1

©2015 by De Gruyter

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