布拉维格子Bravais lattice

立方晶系有 P、I、F 三种；四方晶系有 P、I 两种；正交晶系有 P、C、I、F 四种；单斜晶系有 P、C 两种；三斜、三方（菱方 R）和六方各一种，合计 14 种。之所以没有“四方底心”或“立方底心”等，是因为它们可以等价地选取为更小的已有格子，或者会破坏该晶系应有的对称性。

The cubic system has P, I and F; tetragonal has P and I; orthorhombic has P, C, I and F; monoclinic has P and C; triclinic, trigonal (rhombohedral R) and hexagonal have one each, making 14. There is no 'base-centred tetragonal' or 'base-centred cubic' because such arrangements are equivalent to smaller lattices already listed or would break the symmetry the system requires.

1842 年弗兰肯海姆提出存在 15 种点阵，1848 年法国物理学家奥古斯特·布拉维指出其中两种实际相同，证明三维点阵只有 14 种。二维空间则只有 5 种布拉维格子。在布拉维格子基础上结合 32 种晶体学点群，可得到 230 种空间群。

In 1842 Frankenheim proposed 15 lattices; in 1848 the French physicist Auguste Bravais showed two of them were the same, proving there are only 14 in three dimensions. Two-dimensional space has just 5. Combining the Bravais lattices with the 32 crystallographic point groups gives the 230 space groups.

布拉维格子决定了衍射图的系统消光规律：例如体心格子中 h + k + l 为奇数的衍射消失，面心格子中 h、k、l 奇偶混杂的衍射消失，这是由粉末衍射确定格子类型的依据。金属铜（cF）、α-铁（cI）、氯化铯（cP）分别属于不同的立方格子。

The Bravais lattice fixes the systematic absences in a diffraction pattern: in a body-centred lattice reflections with h + k + l odd vanish, and in a face-centred lattice those with mixed odd and even h, k, l vanish, which is how powder diffraction identifies the lattice type. Copper (cF), α-iron (cI) and caesium chloride (cP) belong to different cubic lattices.