  There are four finite groups that could plausibly play the role of the spin
group in a finite or discrete model of quantum mechanics, namely the four
double covers of the three rotation groups of the Platonic solids. In an
earlier paper I have considered in detail how the smallest of these groups,
namely the binary tetrahedral group, of order 24, could give rise to a
non-relativistic theory that contains much of the structure of the standard
model of particle physics. In this paper I consider how one of the two double
covers of the rotation group of the cube might extend this to a relativistic
theory.
