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Double lattice : ウィキペディア英語版 | Double lattice In mathematics, especially in geometry, a double lattice in is a discrete subgroup of the group of Euclidean motions that consists only of translations and point reflections and such that the subgroup of translations is a lattice. The orbit of any point under the action of a double lattice is a union of two Bravais lattices, related to each other by a point reflection. A double lattice in two dimensions is a p2 wallpaper group. In three dimensions, a double lattice is a space group of the type , as denoted by international notation. == Double lattice packing ==
A packing that can be described as the orbit of a body under the action of a double lattice is called a double lattice packing. In many cases the highest known packing density for a body is achieved by a double lattice. Examples include the regular pentagon, heptagon, and nonagon and the equilateral triangular bipyramid. Włodzimierz Kuperberg and Greg Kuperberg showed that all convex planar bodies can pack at a density of at least by use a double lattice.〔 〕
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Double lattice」の詳細全文を読む
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