Step 1: Recall stereoregularity of polystyrene.
Polystyrene can be atactic, syndiotactic, or isotactic depending on how phenyl groups are arranged relative to the chain.
Step 2: Free radical polymerization.
This process proceeds through random attack on styrene monomers, giving no stereocontrol. The result is an atactic polymer, which is amorphous.
Step 3: Rule out others.
- Ring opening polymerization: not applicable to styrene (not a cyclic monomer).
- Polycondensation: not applicable since styrene polymerizes via addition.
- Ionic polymerization (anionic/cationic): may yield syndiotactic or isotactic structures if catalysts/conditions are controlled, but not atactic.
Step 4: Conclude.
Thus, free radical polymerization is the method for atactic polystyrene.
Final Answer:
\[
\boxed{\text{Free radical polymerization (A)}}
\]