material science - Wyckoff positions and lattice coordinations

Many papers use Wyckoff positions and Space Groups to report atom coordinates, making use of the structure's symmetries to save space in the notation (e.g. diamond = Fd-3m, only).

1. 
   

   How can I reconstruct the whole lattices given such symbols? More specifically I'm interested in the lattices of table 1 from this arxiv paper.

   
   
   


2. 
   

   Where is a good and short source to learn about such reconstructions?