The set of all possible ways to infinitesimally displace the n atoms of a polyatomic gas molecule is a linear space of dimension 3n, because each atom can be independently displaced in each of three orthogonal axis directions. However, some three of these dimensions are just translation of the molecule by an infinitesimal displacement vector, and others are just rigid rotations of it by an infinitesimal angle about some axis. Still others may correspond to relative rotation of two parts of the molecule about a single bond that connects them.
