# Symmorphic space groups

A space group is called ‘symmorphic’ if, apart from the lattice translations, all generating symmetry operations leave one common point fixed. Permitted as *e.g.* *P*2, *Cm*, *P*2/*m*, *P*222, *P*32, *P*23. They are in one to one correspondence with the arithmetic crystal classes.

A characteristic feature of a symmorphic space group is the existence of a special position, the site-symmetry group of which is isomorphic to the point group to which the space group belongs. Symmorphic space groups have no zonal or serial reflection conditions, but may have integral reflection conditions (*e.g.* *C*2, *Fmmm*).

### Note

In the literature sometimes it is found the wrong statement that a symmorphic space group does not contain glide planes or screw *Amm*2 contains *c* glides *x*,1/4,*z* and two-fold screws parallel to [001] and passing at 0,1/4,*z*. This is not even limited to space groups with centered conventional cells: for example, a space group of type *P*422 contains two-fold screws parallel to the two-fold axes.

### See also

Sections 2.2.5 and 8.1.6 of *International Tables for Crystallography, Volume A*

Section 1.4 of *International Tables for Crystallography, Volume C*