  [Abridged] We report Warm Spitzer full-orbit phase observations of WASP-12b
at 3.6 and 4.5 micron. We are able to measure the transit depths, eclipse
depths, thermal and ellipsoidal phase variations at both wavelengths. The large
amplitude phase variations, combined with the planet's previously-measured
day-side spectral energy distribution, is indicative of non-zero Bond albedo
and very poor day-night heat redistribution. The transit depths in the
mid-infrared indicate that the atmospheric opacity is greater at 3.6 than at
4.5 micron, in disagreement with model predictions, irrespective of C/O ratio.
The secondary eclipse depths are consistent with previous studies. We do not
detect ellipsoidal variations at 3.6 micron, but our parameter uncertainties
-estimated via prayer-bead Monte Carlo- keep this non-detection consistent with
model predictions. At 4.5 micron, on the other hand, we detect ellipsoidal
variations that are much stronger than predicted. If interpreted as a geometric
effect due to the planet's elongated shape, these variations imply a 3:2 ratio
for the planet's longest:shortest axes and a relatively bright day-night
terminator. If we instead presume that the 4.5 micron ellipsoidal variations
are due to uncorrected systematic noise and we fix the amplitude of the
variations to zero, the best fit 4.5 micron transit depth becomes commensurate
with the 3.6 micron depth, within the uncertainties. The relative transit
depths are then consistent with a Solar composition and short scale height at
the terminator. Assuming zero ellipsoidal variations also yields a much deeper
4.5 micron eclipse depth, consistent with a Solar composition and modest
temperature inversion. We suggest future observations that could distinguish
between these two scenarios.
