  We approximate the uniform measure on an equilateral triangle by a measure
supported on $n$ points. We find the optimal sets of points ($n$-means) and
corresponding approximation (quantization) error for $n\leq4$, give numerical
optimization results for $n\leq 21$, and a bound on the quantization error for
$n\to\infty$. The equilateral triangle has particularly efficient quantizations
due to its connection with the triangular lattice. Our methods can be applied
to the uniform distributions on general sets with piecewise smooth boundaries.
