  We investigate the phase transition of the dodecahedron model on the square
lattice. The model is a discrete analogue of the classical Heisenberg model,
which has continuous $O(3)$ symmetry. In order to treat the large on-site
degree of freedom $q = 20$, we develop a massively parallelized numerical
algorithm for the corner transfer matrix renormalization group method,
incorporating EigenExa, the high-performance parallelized eigensolver. The
scaling analysis with respect to the cutoff dimension reveals that there is a
second-order phase transition at $T^{~}_{\rm c}=0.4398(8)$ with the critical
exponents $\nu=2.88(8)$ and $\beta=0.21(1)$. The central charge of the system
is estimated as $c=1.99(6)$.
