  We investigate the quantum phase transitions of the transverse-field quantum
Ising model on the triangular lattice and Sierpi\'nski fractal lattices by
employing multipartite entanglement and quantum coherence along with the
quantum renormalization group method. It is shown that the quantum
criticalities of these high-dimensional models closely relate to the behaviors
of the multipartite entanglement and quantum coherence. As the thermodynamic
limit is approached, the first derivatives of multipartite entanglement and
quantum coherence exhibit singular behaviors and the consistent finite-size
scaling behaviors for each lattice are also obtained from the first
derivatives. The multipartite entanglement and quantum coherence are
demonstrated to be good indicators for detecting the quantum phase transitions
in the triangular lattice and Sierpi\'nski fractal lattices. Furthermore, the
factors that determine the relations between the critical exponents and the
correlation length exponents for these models are diverse. For the triangular
lattice, the decisive factor is the spatial dimension, while for the
Sierpi\'nski fractal lattices, it is the Hausdorff dimension.
