  We investigate the high-energy eigenvalue asymptotics quantum graphs
consisting of the vertices and edges of the five Platonic solids considering
two different types of the vertex coupling. One is the standard
$\delta$-condition, the other is the preferred-orientation one introduced in
[ET18]. The aim is to provide another illustration of the fact that the
asymptotic properties of the latter coupling are determined by the vertex
parity by showing that the octahedron graph differs in this respect from the
other four for which the edges at high energies effectively disconnect and the
spectrum approaches the one of the Dirichlet Laplacian on an interval.
