  Several formulas for crossing functions arising in the continuum limit of
critical two-dimensional percolation models are studied. These include Watts's
formula for the horizontal-vertical crossing probability and Cardy's new
formula for the expected number of crossing clusters. It is shown that under
the assumption of conformal invariance, they simplify when the spatial domain
is taken to be the interior of an equilateral triangle. The two crossing
functions can be expressed in terms of an equianharmonic elliptic function with
a triangular rotational symmetry. This suggests that rigorous proofs of Watts's
formula and Cardy's new formula will be easiest to construct if the underlying
lattice is triangular. The simplification in a triangular domain of Schramm's
`bulk Cardy's formula' is also studied.
