  A lack of spatial inversion symmetry gives rise to a variety of
unconventional physics, from noncollinear order and Skyrmion lattice phases in
magnetic materials to topologically-protected surface states in certain band
insulators, to mixed-parity pairing states in superconductors. The search for
exotic physics in such materials is largely limited by a lack of candidate
materials, and often by difficulty in obtaining crystals. Here, we report the
single crystal growth and physical properties of the noncentrosymmetric
tungsten aluminide cage compounds Al$_4$W and Al$_5$W, alongside related
molybdenum aluminides in which spin-orbit coupling should be significantly
weaker. All compounds are nonmagnetic metals. Their high conductivities suggest
the opportunity to find superconductivity at lower temperatures, while the
limits we can place on their transition temperatures suggest that any
superconductivity may be expected to exhibit significant parity mixing.
