Atomistic models of amorphous poly(1,4-trans-butadiene) and isotactic poly(1,2-butadiene) have been obtained at bulk density by carrying out molecular mechanics and molecular dynamics calculations under periodic boundary conditions, along the lines of the previous study of poly(1,4-cis-butadiene). In addition, a model structure has also been obtained for a random copolymer of the trans (55%), cis (35%) and vinyl (10%) units. From the equilibrated structures, the cohesive energy and solubility parameter are calculated. The characteristic intermolecular packing is discussed in detail for these amorphous structures in terms of the pair correlation functions, along with that of poly(1,4-cis-butadiene), which turns out to be significantly different for all four structures. The calculation of conformational statistics of the pure trans structure reveals that it retains the properties predicted by the rotational isomeric state (RIS) theory. Also provided here are the results of conformational analysis on the vinyl structure, for which no thorough RIS analysis has been done. The conformational analysis of the mixed structure shows no significant deviation from the results obtained for the pure trans, cis, or vinyl structures.