  In this paper, we revisit Korn's inequality for the piecewise $H^1$ space
based on general polygonal or polyhedral decompositions of the domain. Our
Korn's inequality is expressed with minimal jump terms. These minimal jump
terms are identified by characterizing the restriction of rigid body mode to
edge/face of the partitions. Such minimal jump conditions are shown to be sharp
for achieving the Korn's inequality as well. The sharpness of our result and
explicitly given minimal conditions can be used to test whether any given
finite element spaces satisfy Korn's inequality, immediately as well as to
build or modify nonconforming finite elements for Korn's inequality to hold.
