So the Space Group does not describe exhaustively the actual structure of a crystal. An example is the following : Crystals of Common Salt (NaCl) crystallize by way of a face-centered cubic lattice (= a lattice consisting of a repetition of a cubical unit of atoms, in this case with atoms at the corners of the cube as well as at the centers of the cube faces). In fact two of these lattices interpenetrate each other (one consisting of Na atoms, the other of Cl atoms). Crystals of the mineral Fluorite (CaF2) on the other hand are also based on two interpenetrating lattices, but in this case one of them is a face-centered cubic lattice (like in Salt) consisting of Ca atoms, and the other is a primitive cubic lattice (i.e. without equivalent atoms in the centers of the cube faces), consisting of F atoms (in fact all the atoms mentioned are, in the cases of Common Salt and Fluorite, ions). However, both Common Salt and Fluorite crystals belong to the same Space Group, namely Fm3m. So in order to determine the structure exhaustively, mentioning of the Space Group must be accompanied by information about the chemical composition (See HOLDEN & MORRISON, 1982, p. 194 and 197).
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