  We investigate magnetic properties of a two-dimensional periodic structure
with Ising spins and antiferromagnetic nearest neighbor interaction. The
structure is topologically equivalent to the Archimedean (3,12^2) lattice. The
ground state energy is degenerate. In some ground states, the spin structure is
translationally invariant, with the same configuration in each unit cell.
Numerical results are reported on specific heat and static magnetic
usceptibility against temperature. Both quantities show maxima at temperature
T>0. They reveal some sensitivity on the initial state in temperatures where
the Edwards--Anderson order parameter is positive. For zero temperature and low
frequency of the applied field, the magnetic losses are negligible. However,
the magnetization curve displays some erratic behavior due to the metastable
states.
