直接空间（或晶体空间）是点空间，En，其中有限实际晶体的结构被理想化为无限完美的三维结构。这个空间与向量空间Vn相关联，其中晶格和平移向量是元素。这是一个欧几里德空间，其中定义了两个向量的标量积。这两个空间通过以下关系连接：（i） 在点空间En的任意两点P和Q上附加向量空间Vn的向量PQ=r。（ii）对于En的每个点P和Vn的每个向量r，有一个精确的En点Q，其中PQ=r成立。（iii）如果R是点空间的第三点，则PQ+QR=PR。 The direct space (or crystal space) is the point space, En, in which the structures of finite real crystals are idealized as infinite perfect three-dimensional structures. To this space one associates the vector space, Vn, of which lattice and translation vectors are elements. It is a Euclidean space where the scalar product of two vectors is defined. The two spaces are connected through the following relations:(i) To any two points P and Q of the point space En a vector PQ = r of the vector space Vn is attached.(ii) For each point P of En and for each vector r of Vn there is exactly one point Q of En for which PQ = r holds.(iii) If R is a third point of the point space, PQ + QR = PR.
