  Regular $A_n$-crystals are certain edge-colored directed graphs which are
related to representations of the quantized universal enveloping algebra
$U_q(\mathfrak{sl}_{n+1})$. For such a crystal $K$ with colors $1,2,...,n$, we
consider its maximal connected subcrystals with colors $1,...,n-1$ and with
colors $2,...,n$ and characterize the interlacing structure for all pairs of
these subcrystals. This is used to give a recursive description of the
combinatorial structure of $K$ and develop an efficient procedure of assembling
$K$.
