  We investigate a two-species Fermi gas in which one species is confined in a
two-dimensional plane (2D) or one-dimensional line (1D) while the other is free
in the three-dimensional space (3D). We discuss the realization of such a
system with the interspecies interaction tuned to resonance. When the mass
ratio is in the range 0.0351<m_2D/m_3D<6.35 for the 2D-3D mixture or
0.00646<m_1D/m_3D<2.06 for the 1D-3D mixture, the resulting system is stable
against the Efimov effect and has universal properties. We calculate key
quantities in the many-body phase diagram. Other possible scale-invariant
systems with short-range few-body interactions are also elucidated.
