  We introduce a new class of intersection graphs, the edge intersection graphs
of paths on a triangular grid, called EPGt graphs. We show similarities and
differences from this new class to the well-known class of EPG graphs. A turn
of a path at a grid point is called a bend. An EPGt representation in which
every path has at most $k$ bends is called a B$_k$-EPGt representation and the
corresponding graphs are called B$_k$-EPGt graphs. We provide examples of
B$_{2}$-EPG graphs that are B$_{1}$-EPGt. We characterize the representation of
cliques with three vertices and chordless 4-cycles in B$_{1}$-EPGt
representations. We also prove that B$_{1}$-EPGt graphs have Strong Helly
number $3$. Furthermore, we prove that B$_{1}$-EPGt graphs are $7$-clique
colorable.
