  Let $K$ denote a field with characteristic 0 and let $T$ denote an
indeterminate. We give a presentation for the three-point loop algebra
$\mathfrak{sl}_2 \otimes K\lbrack T, T^{-1},(T-1)^{-1}\rbrack$ via generators
and relations. This presentation displays $S_4$-symmetry. Using this
presentation we obtain a decomposition of the above loop algebra into a direct
sum of three subalgebras, each of which is isomorphic to the Onsager algebra.
