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In crystallography, the terms crystal system, crystal family, and lattice system each refer to one of several classes of space groups, lattices, point groups, or crystals. Informally, two crystals tend to be in the same crystal system if they have similar symmetries, though there are many exceptions to this. Crystal systems, crystal families, and lattice systems are similar but slightly different, and there is widespread confusion between them: in particular the trigonal crystal system is often confused with the rhombohedral lattice system, and the term "crystal system" is sometimes used to mean "lattice system" or "crystal family". Space groups and crystals are divided into 7 crystal systems according to their point groups, and into 7 lattice systems according to their Bravais lattices. Five of the crystal systems are essentially the same as five of the lattice systems, but the hexagonal and trigonal crystal systems differ from the hexagonal and rhombohedral lattice systems. The six crystal families are formed by combining the hexagonal and trigonal crystal systems into one hexagonal family, in order to eliminate this confusion. ==Overview== A lattice system is generally identified as a set of lattices with the same shape according to the relative lengths of the cell edges (''a'', ''b'', ''c'') and the angles between them (''α'', ''β'', ''γ''). Each lattice is assigned to one of the following classifications (lattice types) based on the positions of the lattice points within the cell: primitive (P), body-centered (I), face-centered (F), base-centered (A, B, or C), and rhombohedral (R). The 14 unique combinations of lattice systems and lattice types are collectively known as the Bravais lattices. Associated with each lattice system is a set of point groups, sometimes called lattice point groups, which are subgroups of the arithmetic crystal classes. In total there are seven lattice systems: triclinic, monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, and cubic. A crystal system is a set of point groups in which the point groups themselves and their corresponding space groups are assigned to the same lattice system. Of the 32 point groups that exist in three dimensions, most are assigned to only one lattice system, in which case the crystal system and lattice system both have the same name. However, five point groups are assigned to two lattice systems, rhombohedral and hexagonal, because both lattice systems exhibit threefold rotational symmetry. These point groups are assigned to the trigonal crystal system. In total there are seven crystal systems: triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. A crystal family is determined by lattices and point groups. It is formed by combining crystal systems which have space groups assigned to the same lattice system. In three dimensions, the crystal families are identical to the crystal systems except the hexagonal and trigonal crystal systems are combined into one hexagonal crystal family. In total there are six crystal families: triclinic, monoclinic, orthorhombic, tetragonal, hexagonal, and cubic. Spaces with less than three dimensions have the same number of crystal systems, crystal families, and lattice systems. In zero- and one-dimensional space, there is one crystal system. In two-dimensional space, there are four crystal systems: oblique, rectangular, square, and hexagonal. The relation between three-dimensional crystal families, crystal systems, and lattice systems is shown in the following table: Caution: There is no "trigonal" lattice system. To avoid confusion of terminology, don't use the term "trigonal lattice"; use the definition that "trigonal lattice" = "hexagonal lattice" ≠ "rhombohedral 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「Crystal system」の詳細全文を読む スポンサード リンク
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