  We study low temperature properties of atomic gases in trimerized optical
kagom\'{e} lattices. The laser arrangements that can be used to create these
lattices are briefly described. We also present explicit results for the
coupling constants of the generalized Hubbard models that can be realized in
such lattices. In the case of a single component Bose gas the existence of a
Mott insulator phase with fractional numbers of particles per trimer is
verified in a mean field approach. The main emphasis of the paper is on an
atomic spinless interacting Fermi gas in the trimerized kagom\'{e} lattice with
two fermions per site. This system is shown to be described by a quantum spin
1/2 model on the triangular lattice with couplings that depend on the bond
directions. We investigate this model by means of exact diagonalization. Our
key finding is that the system exhibits non-standard properties of a quantum
spin-liquid crystal: it combines planar antiferromagnetic order in the ground
state with an exceptionally large number of low energy excitations. The
possibilities of experimental verification of our theoretical results are
critically discussed.
