  The nuclear deformations are of fundamental importance in nuclear physics.
Recently we developed a multi-dimensionally constrained relativistic
Hartree-Bogoliubov (MDCRHB) model, in which all multipole deformations
respecting the $V_4$ symmetry can be considered self-consistently. In this work
we extend this model by incorporating the angular momentum projection (AMP) and
parity projection (PP) to restore the rotational and parity symmetries broken
in the mean-field level. This projected-MDCRHB (p-MDCRHB) model enables us to
connect certain nuclear spectra to exotic intrinsic shapes such as triangle or
tetrahedron. We present the details of the method and an exemplary calculation
for $^{12}$C. We develop a triangular moment constraint to generate the
triangular configurations consisting of three $\alpha$ clusters arranged as an
equilateral triangle. The resulting $^{12}$C spectra are consistent with that
from a triangular rigid rotor for large separations between the $\alpha$
clusters. We also calculate the $B(E2)$ and $B(E3)$ values for low-lying states
and find good agreement with the experiments.
