  Geometrically frustrated clusters of Ising spins of different shapes on a
triangular lattice are studied by exact enumeration and Monte Carlo simulation.
The focus is laid on the ground-state energy and residual entropy behaviors as
functions of the cluster shape and size, as well as the spin value. Depending
on the cluster shape, the residual entropy density on approach to the
thermodynamic limit can either vanish or remain finite and the dependence can
be decreasing, increasing or non-monotonic. Nevertheless, the relative
entropies normalized by the respective thermodynamic limit values turn out to
be little sensitive to the spin value. Some interesting finite-temperature
properties of the clusters are also discussed and attention is drawn to their
magnetocaloric properties.
