  It is evidenced that effective lattice-gas models of hard-core monomers and
dimers afford a proper description of low-temperature features of spin-1/2
Heisenberg diamond and octahedral chains. Besides monomeric particles assigned
within the localized-magnon theory to bound one- and two-magnon eigenstates,
the effective monomer-dimer lattice-gas model additionally includes dimeric
particles assigned to a singlet-tetramer (singlet-hexamer) state as a
cornerstone of dimer-tetramer (tetramer-hexamer) ground state of a spin-1/2
Heisenberg diamond (octahedral) chain. A feasibility of the effective
description is confirmed through the exact diagonalization and
finite-temperature Lanczos methods. Both quantum spin chains display rich
ground-state phase diagrams including discontinuous as well as continuous
field-driven phase transitions, whereby the specific heat shows in vicinity of
the former phase transitions an extraordinary low-temperature peak coming from
a highly-degenerate manifold of low-lying excitations.
