  Liquid crystal elastomer films that morph into cones are strikingly capable
lifters. Thus motivated, we combine theory, numerics, and experiments to
reexamine the load-bearing capacity of conical shells. We show that a cone
squashed between frictionless surfaces buckles at a smaller load, even in
scaling, than the classical Seide/Koiter result. Such buckling begins in a
region of greatly amplified azimuthal compression generated in an outer
boundary layer with oscillatory bend. Experimentally and numerically, buckling
then grows sub-critically over the full cone. We derive a new thin-limit
formula for the critical load, $\propto t^{5/2}$, and validate it numerically.
We also investigate deep post-buckling, finding further instabilities producing
intricate states with multiple Pogorelov-type curved ridges arranged in
concentric-circles or Archimedean spirals. Finally, we investigate the forces
exerted by such states, which limit lifting performance in active cones.
