I. INTRODUCTION There is a wide range of colloidal particles with platelet-like shape, including materials such as gibbsite [1] and certain clays including montmorillonite, laponite and hydrotalcite [2–7]. Clays are some of the most abundant minerals on the Earth’s surface and are used as pharmaceuticals, cosmetics and catalysts. There is much current interest in the use of platelets in nanocomposite materials, e.g. the nematic phase of sterically stabilised gibbsite platelets may be used as a template for gibbsite-polymer nanocomposites with nematic order [8]. Interest in platelet dispersions is also present in geophysics [9], biomedicine [10] and liquid crystal display (LCD) technology [11]. Understanding the liquid crystalline phase behaviour of systems of non-spherical particles [12–14] is an important topic in modern condensed matter physics. One of the most cele- brated cases of a phase transition in such systems is the isotropic-nematic ( I - N ) transition. For athermal model systems, where the particle interactions are hard core, phase transi- tions arise purely from entropic contributions to the free energy and the phase behaviour is governed solely by density and is independent of temperature. Such models can be used to describe lyotropic liquid crystals and phase transitions such as the I - N transition. Onsager showed how the formation of liquid crystalline phases can be understood on the basis of pair interactions between the constituents of the material [15–17]. He considered the hard platelet fluid but we know that unlike the case of rod-like particles, his second-virial theory does not produce quantitatively correct results for the equation of state and the I - N coexistence densities. Onsager himself noted that higher virial contributions are important for obtaining reliable results, estimating the ratio B$_{3}$/B 2 at O (1), with B$_{2}$ and B$_{3}$ being the second and third virial coefficients, respectively. Nevertheless, the second-virial theory has been employed to investigate the monodisperse platelet system [18, 19]. In Ref. [18] a numerical approach was used to calculate the phase diagram of platelets for varying thickness, including the case of zero thickness. This is complemented by a calculation for the equation of state in both the I and N phases for van- ishingly thin platelets in Ref. [19]. The first off-lattice simulation study of the I - N transition for infinitely thin platelets was carried out in Ref. [20]. This showed that the phase diagram differs substantially from the Onsager prediction and that the I - N transition is actually much more weakly first order and occurs at lower densities than predicted theoretically. 2