2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/19517The phase diagram of a polydisperse mixture of uniaxial rod-like and plate-like hard parallelepipeds is determined for aspect ratios $κ=5$ and 15. All particles have equal volume and polydispersity is introduced in a highly symmetric way. The corresponding binary mixture is known to have a biaxial phase for $κ=15$, but to be unstable against demixing into two uniaxial nematics for $κ=5$. We find that the phase diagram for $κ=15$ is qualitatively similar to that of the binary mixture, regardless the amount of polydispersity, while for $κ=5$ a sufficient amount of polydispersity stabilizes the biaxial phase. This provides some clues for the design of an experiment in which this long searched biaxial phase could be observed.4 pages, 5 eps figure files, uses RevTeX 4 styleSoft Condensed MatterStatistical Mechanicstext