  Stembridge characterized regular crystals associated with a simply-laced
generalized Cartan matrix (GCM) in terms of local graph-theoretic quantities.
We give a similar axiomatization for $B_2$ regular crystals and thus for
regular crystals associated with a finite GCM except $G_2$ and an affine GCM
except $A^{(1)}_{1},G^{(1)}_{2},A^{(2)}_{2},D^{(3)}_4$.
