The phase behavior of rod-plate mixtures was investigated using model systems containing unambiguously rod-and plate-shaped colloids. We find that the theoretically disputed biaxial nematic phase is unstable with respect to demixing into an isotropic and two uniaxial nematic phases. The phase behavior at very high densities is exceptionally rich and includes the coexistence of up to four different liquid crystalline phases, which stem from the coupling between the employed particle shapes and polydispersity. PACS numbers: 82.70.Dd, 64.70.Md The entropy-driven formation of the uniaxial nematic phase in suspensions of rodlike or platelike particles has been established in theory [1] and in simulations [2], as well as in experiments [3][4][5][6] in the course of this century. The probably even richer liquid crystalline phase behavior exhibited by mixtures of rodlike and platelike particles, on the other hand, is currently subject to debate. The central question here is whether or not there exists a so-called biaxial nematic in these mixtures, in which both rods and plates are orientationally ordered but in mutually perpendicular directions. In earlier theoretical studies this biaxial phase was found to be stable over a broad range of compositions [7][8][9][10]. Recent theoretical study [11] and simulations [12] show that, at least in some cases, the biaxial phase may be unstable with respect to demixing into two separate uniaxial phases of predominantly rods and plates, respectively. On the part of experimental evidence, indications for biaxiality have been reported by Yu and Saupe [13] for a system containing both cylindrical and lamellar micelles. There is, however, some doubt [10,12] as to whether their observations are indicative of a biaxial phase transition or rather relate to a change in shape of the inherently "soft" micelles. In principle, model systems of inorganic colloids give the opportunity to study the phase behavior of unambiguously rodlike and platelike particles. In fact, the first experimental evidence for a uniaxial nematic phase was observed already in the 1920s in a suspension of inorganic vanadium pentoxide rods by Zocher [3]. However, a corresponding hard plate model system, i.e., consisting of particles with a short range repulsive interaction which seems crucial for exhibiting the unhindered isotropic to nematic ͑I-N͒ phase transition [14,15], has been lacking until recently. In this study we adopt a novel model system of platelike colloids which does show the I-N transition in its unmixed form [6]. Combining this system with its rodlike analog allows us to investigate the liquid crystalline phase behavior of a mixture of such plainly rod-and plate-shaped particles.The origin of liquid crystal stability in hard rod/plate mixtures is closely related to the case of the pure components, i.e., for rods and plates separately. Such spontaneous alignment in systems of nonattracting anisometric particles, which may seem counterintuitive at first thought, was first explained by Onsager [1] in th...