How are the hybrid orbitals of sulfur hexafluoride shaped?
If you limit consideration to hybridization of atomic orbitals, a good reference to see is On the role of d orbitals in sulfur hexafluoride J. Am. Chem. Soc., 1986, 108 (13), pp 3586–3593.

First, it is found that of the 6 valence electrons that atomic sulfur has (two 3s and four 3p), in SF6 a total of 3.1 electrons worth of electron probability density remain in sulfur atomic orbitals.  

Of the 3.1 electrons:

0.97 are in the 3s orbital

1.82 are in 3p orbitals  

0.24 are in 3d orbitals

and small fractions are in 4s, 4p and 4 d orbitals.  

For a more recent study, see Theory of Hypervalency: Recoupled Pair Bonding in SFn (n = 1−6) J. Phys. Chem. A, 2009, 113 (27), pp 7915–7926