Closest packing of spheres

Japanese: 最密充てん(最密充塡) - さいみつじゅうてん（英語表記）closest packing of spheres

The structure in which spheres of the same size are most densely packed in three dimensions is called the closest packed structure of spheres. To pack spheres as densely as possible on the same plane, they are arranged so that three adjacent spheres are at the three corners of an equilateral triangle, and six spheres touch each other on each side. This is equivalent to the most densely packed arrangement of circles of the same size on a plane, with the percentage of the circles being π/2, or 91%. The most densely packed three-dimensional arrangement of spheres is when the second layer of spheres is stacked parallel to the center of gravity of the equilateral triangle of the closest packed layer of spheres.

Source: Heibonsha World Encyclopedia, 2nd Edition Information

Japanese:

同じ大きさの球を，立体的に最も密に詰めた構造を球の最密充てん構造という。球を同一平面上にできる限り密に詰めるには，隣りあう3球が正三角形の3隅にくるように並べ，どの球の周りにも6個の球が接するようにする。これは，平面上で同じ大きさの円を最も密に詰める並べ方に相当し，円の占める割合はπ/2，すなわち91％になる。球の三次元的な最密な詰め方は，球の最密な層の正三角形の重心の真上に，第2層の球がくるように平行に積み重ねたものである。

出典　株式会社平凡社世界大百科事典第２版について　情報

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