晶系Crystal system

立方（a = b = c，α = β = γ = 90°，4 条三重轴）：NaCl、金刚石；四方（a = b ≠ c，均 90°，1 条四重轴）：金红石 TiO₂、锡石；正交（a ≠ b ≠ c，均 90°，3 条二重轴）：硫磺、文石；单斜（a ≠ b ≠ c，α = γ = 90° ≠ β，1 条二重轴）：石膏、蔗糖；三斜（全不等，无轴）：硫酸铜晶体；三方（1 条三重轴）：方解石、石英；六方（a = b ≠ c，γ = 120°，1 条六重轴）：石墨、冰、镁。

Cubic (a = b = c, all angles 90°, four threefold axes): NaCl, diamond. Tetragonal (a = b ≠ c, 90°, one fourfold axis): rutile TiO₂, cassiterite. Orthorhombic (a ≠ b ≠ c, 90°, three twofold axes): sulfur, aragonite. Monoclinic (a ≠ b ≠ c, α = γ = 90° ≠ β, one twofold axis): gypsum, sucrose. Triclinic (nothing equal, no axes): copper sulfate pentahydrate. Trigonal (one threefold axis): calcite, quartz. Hexagonal (a = b ≠ c, γ = 120°, one sixfold axis): graphite, ice, magnesium.

19 世纪初魏斯根据晶体外形的对称轴提出晶系分类；1830 年赫塞尔推导出 32 种晶体学点群（晶类）。晶体中只允许 1、2、3、4、6 次旋转对称，因为五次或七次以上的旋转对称无法用平行六面体填满空间，这一“晶体学限制定理”使晶系数目有限。

In the early nineteenth century Weiss classified crystals by the symmetry axes of their shapes, and in 1830 Hessel derived the 32 crystallographic point groups (crystal classes). Only 1-, 2-, 3-, 4- and 6-fold rotations are allowed, because fivefold or higher than sixfold symmetry cannot fill space with parallelepipeds; this crystallographic restriction theorem limits the number of systems.

晶系与物理性质密切相关：立方晶体光学各向同性，其他晶系有双折射（如方解石的双像）；只有缺少对称中心的晶类才可能有压电性（如石英，用于钟表振子）和倍频效应。药物多晶型可能属于不同晶系，溶解度和稳定性不同。

Crystal system strongly affects physical properties: cubic crystals are optically isotropic, while the others are birefringent, as in calcite's double image; only classes without an inversion centre can be piezoelectric (like quartz in watch oscillators) or show frequency doubling. Polymorphs of a drug may belong to different systems with different solubility and stability.