Is a formula possible for determining the volume of a cuboid from only the values of its perimeter, its surface area and, perhaps, its space diagonal? I have derived formulae that require an additional property of the cuboid, but that does not suit my objective. I wondered if there is any merit in considering solid trigonometry in which, one corner of the cuboid is positioned at the centre of a sphere, with its edges aligned with the 3-D frame of reference, also located at the spherical centre and the radial vector of the sphere acting as the space diagonal of the cuboid.