  Regular $A_n$-, $B_n$- and $C_n$-crystals are edge-colored directed graphs,
with ordered colors $1,2,...,n$, which are related to representations of
quantized algebras $U_q(\mathfrak{sl}_{n+1})$, $U_q(\mathfrak{sp}_{2n})$ and
$U_q(\mathfrak{so}_{2n+1})$, respectively. We develop combinatorial methods to
reveal refined structural properties of such objects.
  Firstly, we study subcrystals of a regular $A_n$-crystal $K$ and characterize
pairwise intersections of maximal subcrystals with colors $1,...,n-1$ and
colors $2,...,n$. This leads to a recursive description of the structure of $K$
and provides an efficient procedure of assembling $K$.
  Secondly, using merely combinatorial means, we demonstrate a relationship
between regular $B_n$-crystals (resp. $C_n$-crystals) and regular symmetric
$A_{2n-1}$-crystals (resp. $A_{2n}$-crystals).
