  The ground state, magnetization scenario and the local bipartite quantum
entanglement of a mixed spin-$1/2$ Ising--Heisenberg model in a magnetic field
on planar lattices formed by identical corner-sharing bipyramidal plaquettes is
examined by combining the exact analytical concept of generalized
decoration-iteration mapping transformations with Monte Carlo simulations
utilizing the Metropolis algorithm. The ground-state phase diagram of the model
involves six different phases, namely, the standard ferrimagnetic phase, fully
saturated phase, two unique quantum ferrimagnetic phases, and two
macroscopically degenerate quantum ferrimagnetic phases with two chiral degrees
of freedom of the Heisenberg triangular clusters. The diversity of ground-state
spin arrangement is manifested themselves in seven different magnetization
scenarios with one, two or three fractional plateaus whose values are
determined by the number of corner-sharing plaquettes. The low-temperature
values of the concurrence demonstrate that the bipartite quantum entanglement
of the Heisenberg spins in quantum ferrimagnetic phases is field independent,
but twice as strong if the Heisenberg spin arrangement is unique as it is
two-fold degenerate.
