  This work investigates the class of prime star multiplexes, in which each of
its layers $i$, $i=1,2, \ldots M$, consists of a regular cycle graph where any
node has $2J_i$ neighbors. In a process that does not affect the cyclic
topology, it is assumed that, before the multiplex is assembled, the nodes are
labeled differently in each individual layer. As the setup requires that all
representations of the same node in the different $M$ layers must be linked by
inter-layers connections, the resulting multiplex pattern can be highly
complex. This can be better visualized if one assumes that in one layer the
nodes are labeled in the sequentially ascending order and that the nodes with
the same label are drawn on the top of the other, so that all inter-layer
connections are represented by vertical lines. In such cases, the other $M-1$
layers are characterized by long distance shortcuts. As a consequence, in spite
of sharing the same internal topological structure, the multiplex ends up with
very dissimilar layers. For prime number of nodes, a regular star geometry
arises by requiring that the neighbor labels of the $M-1$ layers differ by a
constant value $p_i>1$. For $M=2$, we use analytical and numerical approaches
to provide a thorough characterization of the multiplex topological properties,
of the inter layer dissimilarity, and of the diffusive dynamical processes
taking place on them. For the sake of definitiveness, it is considered that
each node in the sequentially labeled layer is characterized by $J_1\geq1$. In
the other layer, we fix $J_2\equiv1$, while $p>1$ becomes a proxy of layer
dissimilarity.
