  The classic Dyck triangle, the Catalan triangle, and the Catalan convolution
matrix are plane projections of the multidimensional Dyck triangle. In the Dyck
path, each node is uniquely determined by two of four interrelated parameters:
(i) the position of the current parenthesis, (ii) the current unbalance of the
parentheses, (iii) the number of viewed left parentheses, and (iv) the same for
right parentheses. The last two parameters can be redefined, respectively, as
the index of the current Catalan number and the index of the summand in the
decomposition of the Catalan number into the sum of squares (Dyck squares). For
the 4D Dyck triangle, we consider six 2D projections (some of them are not yet
in demand) and four 3D projections.
