  Using the fact that the energy eigenstates of the equilateral triangle
infinite well (or billiard) are available in closed form, we examine the
connections between the energy eigenvalue spectrum and the classical closed
paths in this geometry, using both periodic orbit theory and the short-term
semi-classical behavior of wave packets. We also discuss wave packet revivals
and show that there are exact revivals, for all wave packets, at times given by
$T_{rev} = 9 \mu a^2/4\hbar \pi$ where $a$ and $\mu$ are the length of one side
and the mass of the point particle respectively. We find additional cases of
exact revivals with shorter revival times for zero-momentum wave packets
initially located at special symmetry points inside the billiard. Finally, we
discuss simple variations on the equilateral
($60^{\circ}-60^{\circ}-60^{\circ}$) triangle, such as the half equilateral
($30^{\circ}-60^{\circ}-90^{\circ}$) triangle and other `foldings', which have
related energy spectra and revival structures.
