I have two questions: first, whether the LAMMPS provide a method to create region shapes of tetrahedron , octahedron and cubo-octahedron. Second, whether the calculation of velocity autocorrelation function is included in LAMMPS.
The answer to all your questions is no. However, if you know the
formulas to determine whether a point is inside/outside
the shapes you mention, then adding a new region
option to LAMMPS is about the easiest feature to add.