  Anisotropy is important for the existence of true long range order in two
dimensional (2D) systems. This is firmly exemplified by the $q$-state clock
models in which discreteness drives the quasi-long range order into a true long
range order at low temperature for $q> 4$. Previously we studied 2D edge-cubic
spin model, which is one of the discrete counterpart of the continuous
Heisenberg model, and observed two finite temperature phase transitions, each
corresponds to the breakdown of octahedral ($O_h$) symmetry and $C_{3h}$
symmetry, which finally freezes into ground state configuration. The present
study investigates discret models with polyhedral symmetry, obtained by e
equally partioning the $4\pi$ of the solid angle of a sphere. There are five
types of models if spins are only allowed to point to the vertices of the
polyhedral structures such as Tetrahedron, Octahedron, Hexahedron, Icosahedron
and Dodecahedron. By using Monte Carlo simulation with cluster algorithm we
calculate order parameters and estimate the critical temperatures exponents of
each model. We found a systematic decrease in critical temperatures as the
number of spin states increases (from the Tetrahedral to Dodecahedral spin
model).
