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We use computer simulations to study the existence and stability of a biaxialnematic $N_b$ phase in systems of hard polyhedral cuboids, triangular prisms,and rhombic platelets, characterized by a long ($L$), medium ($M$), and short($S$) particle axis. For all three shape families, we find stable $N_b$ statesprovided the shape is not only close to the so-called dual shape with $M =\sqrt{LS}$ but also sufficiently anisotropic with $L/S>9,11,14, 23$ for rhombi,prisms, and cuboids, respectively, corresponding to anisotropies not consideredbefore. Surprisingly, a direct isotropic-$N_b$ transition does not occur inthese systems due to a destabilization of $N_b$ by a smectic (for cuboids andprisms) or a columnar (for platelets) phase at small $L/S$, or by anintervening uniaxial nematic phase at large $L/S$. Our results are confirmed bya density functional theory provided the third virial coefficient is includedand a continuous rather than a discrete (Zwanzig) set of particle orientationsis taken into account.

Hard competition: stabilizing the elusive biaxial nematic phase in suspensions of colloidal particles with extreme lengths