# Space Group H3

Ralf W. Grosse-Kunstleve rwgk at laplace.csb.yale.edu
Tue Apr 21 20:34:52 EST 1998

```>R3 and variants corespond to the rhombohedral setting which is a special
>case of hexagonal.

Sorry, but this is wrong.

R3 is strictly a trigonal space group.

Take space groups P222 and I222. Both are orthorhombic. The first is
primitive, the second is body-centred. Now, it is possible to describe
space group I222 with a primitve cell. The rotation axes are no longer
parallel to the basis vectors, that why nobody likes to use such a
setting.

Now take P3 and R3. Both trigonal. Normally, both space group are
described using a hexagonal basis (the lattice defined by the basis
has hexagonal symmetry, but the space groups P3 and R3 do not).
Like it is possible to describe I222 with a primitive basis, it is
possible to describe R3 with a primitive basis. In the latter case
however, the 3-fold axis can be made parallel [1,1,1] (the body
diagonal), and therefore people sometimes find this setting useful
and it was included in the Int. Tables.

Any space group can be described in an infinite number of different
ways. For most space groups, only one setting is of practical importance.
The R-centred trigonal space groups are the exception.

Ralf

```