  Percolation on a plane is usually associated with clusters spanning two
opposite sides of a rectangular system. Here we investigate three-leg clusters
generated on a square lattice and spanning the three sides of equilateral
triangles. If the position and orientation of the triangles relative to the
lattice are uniformly randomized, one obtains an efficient method of
determining the percolation threshold, on par with the most advanced Monte
Carlo methods developed for the rectangular geometry. The universal crossing
probability for three-leg clusters is geometry-independent, which opens a way
for further improvements of the method.
