  Type II strings in D=5 contain particle-like 1/8 supersymmetric BPS states.
In this note we give a string-network representation of such states by
considering (periodic) non-planar $(p,q,r)$-string networks of eight
dimensional type II string theory on $T^3$. We obtain the BPS mass formula of
such states, in terms of charges and generating-vectors of the torus, and show
its invariance under an $SL(3, Z)\times SL(3, Z)$ group of transformations.
Results are then generalized to string-networks associated with the $SL(5, Z)$
$U$-duality in seven dimensions. We also discuss reinterpretation of the above
$(D=5)$ mass formula in terms of BPS states in world-volume theories of
$U2$-branes in D=8.
