We investigate the phase transition of the dodecahedron model on the square lattice. The model is a discrete analog 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_{c}^{}=0.4398(8) with the critical exponents ν=2.88(8) and β=0.21(1). The central charge of the system is estimated as c=1.99(6).