A prominent feature of coronaviruses is the presence of a large glycoprotein spike (S) protruding from the viral particle. The specific interactions of a material with S determine key aspects such as its possible role for indirect transmission or its suitability as a virucidal material. Here, we consider all-atom molecular dynamics simulations of the interaction between a polymer surface (polystyrene) and S in its up and down conformations. Polystyrene is a commonly used plastic found in electronics, toys, and many other common objects. Also, previous atomic force microscopy (AFM) experiments showed substantial adhesion of S over polystyrene, stronger than in other common materials. Our results show that the main driving forces for the adsorption of the S protein over polystyrene were hydrophobic and π-π interactions with S amino acids and glycans. The interaction was stronger for the case of S in the up conformation, which exposes one highly flexible receptor binding domain (RBD) that adjusts its conformation to interact with the polymer surface. In this case, the interaction has similar contributions from the RBD and glycans. In the case of S in the down conformation, the interaction with the polystyrene surface was weaker and it was dominated by glycans located near the RBD. We do not find significant structural changes in the conformation of S, a result which is in deep contrast to our previous results with another hydrophobic surface (graphite). Our results suggest that SARS-CoV-2 virions may adsorb strongly over plastic surfaces without significantly affecting their infectivity.