Unlike the name suggests, paratacamite is not a polymorph of atacamite, clinoatacamite and botallackite. It was originally believed to be one, but it was recently discovered that it contains essential zinc in its composition, which stabilizes the structure. A zinc-free mineral with the structure of paratacamite does not exist. 

 In atacamite, botallackite and clinoatacamite, on the other hand, zinc is not an essential constituent. Entirely zinc-free phases are (meta)stable enough to exist (although naturally occurring material usually contains more or less zinc replacing for copper). 

 Reference: see http://www.mindat.org/min-3115.html (last entry in the reference section)