  Multi-band touchings such as 3-band, 6-band and 8-band touchings together
with the emergence of high pseudospin fermions were predicted recently at
high-symmetry points in three-dimensional space. In this paper, we propose a
simple cubic model whose unit cell contains three atoms. There are 6 bands in
the system due to the spin degrees of freedom. The 4-band and 2-band touchings
are realized at high-symmetry points, where we derive low-energy theories,
demonstrating the emergence of pseudospin-3/2 fermions and Weyl fermions,
respectively. Away from the high-symmetry points, we find critical Weyl
fermions present exactly at the boundary between the type-I and type-II Weyl
fermions. This critical Weyl fermion transforms into the type-I or type-II Weyl
fermion once the magnetic field is applied.
