  We construct the set of all general (i.e. not necessarily rank 1) symmetric
informationally complete (SIC) positive operator valued measures (POVMs). In
particular, we show that any orthonormal basis of a real vector space of
dimension d^2-1 corresponds to some general SIC POVM and vice versa. Our
constructed set of all general SIC-POVMs contains weak SIC-POVMs for which each
POVM element can be made arbitrarily close to a multiple times the identity. On
the other hand, it remains open if for all finite dimensions our constructed
family contains a rank 1 SIC-POVM.
