  We model the quasicrystal-related structure CaCd$_6$, a bcc packing of
icosahedral clusters containing tetrahedra which undergo orientational
orderings at T<100 K. We use general schemes to evaluate an effective
Hamltonian for inter-tetrahedron orientations, based on all-atom relaxations,
either in terms of discrete cluster orientations, or of continuous rotation
angles. The effective Hamiltonian is used in Monte Carlo simulations to find
the (complex) ground state ordering pattern as a function of pressure. A
preliminary investigation of thermal transitions found (in part of the pressure
range) two different first-order transitions occurring below 100 K.
