  Magnetization process and adiabatic demagnetization of the antiferromagnetic
Ising spin clusters with the shape of regular polyhedra (Platonic solids) are
exactly examined within the framework of a simple graph-theoretical approach.
While the Ising cube as the only unfrustrated (bipartite) spin cluster shows
just one trivial plateau at zero magnetization, the other regular Ising
polyhedra (tetrahedron, octahedron, icosahedron and dodecahedron) additionally
display either one or two intermediate plateaux at fractional values of the
saturation magnetization. The nature of highly degenerate ground states
emergent at intermediate plateaux owing to a geometric frustration is
clarified. It is evidenced that the regular Ising polyhedra exhibit a giant
magnetocaloric effect in a vicinity of magnetization jumps, whereas the Ising
octahedron and dodecahedron belong to the most prominent geometrically
frustrated spin clusters that enable an efficient low-temperature refrigeration
by the process of adiabatic demagnetization.
