  Nuclear site analysis methods are used to enumerate the normal modes of
$ABX_{3}$ perovskite polymorphs with octahedral rotations. We provide the modes
of the fourteen subgroups of the cubic aristotype describing the Glazer
octahedral tilt patterns, which are obtained from rotations of the $BX_{6}$
octahedra with different sense and amplitude about high symmetry axes. We
tabulate all normal modes of each tilt system and specify the contribution of
each atomic species to the mode displacement pattern, elucidating the physical
meaning of the symmetry unique modes. We have systematically generated 705
schematic atomic displacement patterns for the normal modes of all 15 (14
rotated + 1 unrotated) Glazer tilt systems. We show through some illustrative
examples how to use these tables to identify the octahedral rotations,
symmetric breathing, and first-order Jahn-Teller anti-symmetric breathing
distortions of the $BX_{6}$ octahedra, and the associated Raman selection
rules. We anticipate that these tables and schematics will be useful in
understanding the lattice dynamics of bulk perovskites and would serve as
reference point in elucidating the atomic origin of a wide range of physical
properties in synthetic perovskite thin films and superlattices.
