  It is noted that the Poincar\'e sphere for polarization optics contains the
symmetries of the Lorentz group. The sphere is thus capable of describing the
internal space-time symmetries dictated by Wigner's little groups. For massive
particles, the little group is like the three-dimensional rotation group, while
it is like the two-dimensional Euclidean group for massless particles. It is
shown that the Poincar\'e sphere, in addition, has a symmetry parameter
corresponding to reducing the particle mass from a positive value to zero. The
Poincar\'e sphere thus the gives one unified picture of Wigner's little groups
for massive and massless particles.
