Density of the <i>p2gg</i>-4c1 packing of ellipses (II)

<jats:title>Abstract</jats:title> <jats:p>As the second paper of the series, the first of which was published in 1997 (M. Tanemura, T. Matsumoto, Density of the <jats:italic>p2gg</jats:italic>-4c1 packing of ellipses (I). <jats:italic>Z. Kristallogr.</jats:italic> <jats:bold>1997</jats:bold>, <jats:italic>212</jats:italic>, 637), the <jats:italic>p2gg</jats:italic>-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 <jats:italic>p2gg</jats:italic>-4c1(b) packing of ellipses does not exceed the maximum density <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_zkri-2015-1880_fx_001.jpg" /> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block"> <m:mrow> <m:mi>ρ</m:mi> <m:mtext> </m:mtext> <m:mo>=</m:mo> <m:mtext> </m:mtext> <m:mi>π</m:mi> <m:mn>/</m:mn> <m:msqrt> <m:mrow> <m:mn>12</m:mn> </m:mrow> </m:msqrt> </m:mrow> </m:math> <jats:tex-math>$\rho \; = \;\pi /\sqrt {12} $</jats:tex-math> </jats:alternatives> </jats:inline-formula> through numerical computations and series expansions. It is also shown that the <jats:italic>p2gg</jats:italic>-2a2 packing of ellipses has the similar properties and that it is considered as a special case of <jats:italic>p2gg</jats:italic>-4c1(b) packing. The method of computing the density for every parameter values of aspect ratio and tilt angle is given.</jats:p>