In 1970, Freiser made the theoretical prediction that a biaxial nematic phase could exist. In auniaxial nematic, only one particle axis is aligned but with a biaxial nematic, all three molecular axes are aligned. This phase is expected to occur for particle whose shape is intermediate between that of a disc and a rod. Board and bent-core particles are examples of such structures. Despite extensive experimental investigation, however, very few biaxial nematic systems have been found.Yu and Saupe  have shown the occurrence of a biaxial nematic phase generated for a lyotropic system. Similarly van der Pol observed a biaxial nematic phase in a colloidal suspension of board-like goethite particles . For thermotropic, molecular systems, however, the situation is less clear-cut. Merkel et al.,  and Figueirinhas et al.,  claim that Tetrapodes have can exhibit a biaxial nematic phase, whilst Acharya et al.,  and Prasad et al.,  have also suggested the occurrence of this same phase with bent-core molecules, though experimental uncertainty still exist. With regards to theoretical predictions of the biaxial nematic transition, one notes in particular the work of Taylor and Herzfeld  on hard sphero-platelets, which predicts a rich phase diagram, notably containing an unusual discotic smectic phase.To date there are few simulations of board-like models, such as Vanakaras et al.,  being arecent exception, developing a phase diagram for hard board-like colloids. Similarly, Escobedo has produced a phase diagram of hard cuboids.We present molecular dynamics simulation results on a short range repulsive fused-hexagonmodel, somewhat resembling hard boards. Depending on the geometry of the board, we observe uniaxial and biaxial nematics, smectics A and C, a biaxial smectic phase and a columnar phase. Possibly the most interesting result is the existence of the theoretically predicted discoticsmectic.We further investigated the effect of applying both external fields and shears to several of the structures. The former, among other things, aided the alignment of the particles in the phase, removing dislocations. The shear was also seen to increase biaxial ordering, however, it also demonstrates an ability to introduce clear layer fractures, seen when shearing forces became overly dominant. An applied electrical field was able to induce isotropic!biaxial nematic and biaxial smectic switching. Finally we consider briefly less-symmetric arrangements of fused hexagons, including chiral particles. These systems proved hard to equilibrate but discotic nematic phases were observed for certain structures. Chiral clusters were also observed, however, no globally chiral phase was found. Columnar structures were also seen, but showing a weak overall alignment as columnstended to point along several directions.