  The so-called quantum Cheshire Cat is a scenario where a photon, identified
with a cat, and a component of its polarization, identified with the grin of
that cat, are separated. We observe that the same techniques can be used to
separate two orthogonal components of polarization of a photon, on an average.
We identify these polarization components of the photon as the grin and snarl
of the cat for ease of comprehension. A gedanken experiment is presented in
which we simultaneously tune the input polarizations of the photon in the two
arms of a Mach-Zehnder interferometer. It is noted that for two particular
choices of photon polarization, the presence of the two components gets
reversed in the two arms. This reversal of the grin and the snarl occurs before
the polarization components even interact with the tuners, i.e., before the
choice of which arm each should be in is made.
