  Postulating that spacetime is discrete, we assume that physical space is
described by a 3-dimensional cubic lattice.The corresponding symmetry group of
rotations has order 24 and motivates the introduction of a cubic shaped graph
with 27 vertices and 351 edges. We call this graph the elementary particle cube
(EPC) and consider the vertices as tiny cells that pre-elementary particles
called preons can occupy and the edges as interactions between preons. The 23
nontrivial members of the symmetry group naturally associate with the 23 basic
elementary particles. We assume that each elementary particle is described by a
unique subgraph of the EPC. The particular subgraph is determined by symmetry
and the particle's mass. We postulate that the particle mass is a certain
function of the lengths of the edges in the graph representing the particle.
This correspondence between particle graphs and mass appears to be quite
accurate and gives a reason why leptons and quarks come in three generations.
In this way, the basic elementary particles emerge in a natural way from a few
simple principles. The paper ends with a discussion of hadrons, which as in the
standard model, are composite systems of quarks.
