A Fourier transform spectrum of the lowest frequency degenerate fundamental of CH3CD3 (upsilon(12)=1<--0) near 680 cm(-1) has been measured in order to investigate the vibration-torsion-rotation effects in a symmetric toy. The spectrum was recorded at an instrumental resolution of 0.0024 cm(-1) using a modified Bomem spectrometer. The temperature and pressure of the sample were 130 K and 0.4 Torr, respectively. Although the intrinsic tunneling splittings in each (J'<--J ") multiplet are the order of 0.002 cm(-1) or smaller, the splittings typically observed for an intermediate J " of 10 are two to three orders of magnitude larger. These splittings are caused primarily by the Coriolis interaction between the torsional stack of levels upsilon(6)=0,1,2,... for upsilon(12)=1 and the corresponding stack for upsilon(12)=0. The shift of each upper level (upsilon(12)=1, l; J, upsilon(6)=0,K,sigma) is seen to be a sensitive function of (l;K,sigma), where a labels the torsional sublevels. Because of near degeneracies between the upper level and its interaction partner with (upsilon(12)=0, upsilon(6)=3), four different (l;K,sigma) torsion-rotation series are resonantly perturbed. For three of these cases, perturbation-allowed (upsilon(6)=3<--0) torsional transitions have been identified. Over 2000 transitions belonging to the nu(12) and 3 nu(6) bands have been assigned. The measurements from the present experiment and frequencies from previously reported studies in the ground vibrational state were fitted to within experimental uncertainty using an effective Hamiltonian discussed earlier in connection with CH3SiH3 [Moazzen-Ahmadi et al., J. Mol. Spectrosc. 137, 166 (1989)]. Several Coriolis parameters were determined. In particular, the experimental value of <(zeta)over tilde>(z)(12)=0.248 657(50) is in good agreement with the calculated value of 0.24, whereas the experimental value of <(zeta)over tilde>(x)(6.12)=0.2245(45) is in clear disagreement with the calculated value of 0.56.