  There seems to be a one to one correspondence between the phases of atomic
and molecular matter (AMOM) and vortex matter (VM) in superfluids and
superconductors. Crystals, liquids and glasses have been experimentally
observed in both AMOM and VM. However, quasi-crystals also exist in AMOM, thus
a new phase of vortex matter is proposed here: the vortex quasi-crystal. It is
argued that vortex quasi-crystals are stabilized due to imposed quasi-periodic
potentials in large samples or due to boundary and surface energy effects for
samples of special shapes and sizes. For finite size samples, it is proposed
that a phase transition between a vortex crystal and a vortex quasi-crystal
occurs as a function of magnetic field and temperature as the sample size is
reduced.
