  Let $\mathbb{K}$ denote an algebraically closed field. Let $V$ denote a
vector space over $\mathbb{K}$ with finite positive dimension. By a Leonard
triple on $V$ we mean an ordered triple of linear transformations in ${\rm
End}(V)$ such that for each of these transformations there exists a basis of
$V$ with respect to which the matrix representing that transformation is
diagonal and the matrices representing the other two transformations are
irreducible tridiagonal. There is a family of Leonard triples said to have
QRacah type. This is the most general type of Leonard triple. We classify the
Leonard triples of QRacah type up to isomorphism. We show that any Leonard
triple of QRacah type satisfies the $\mathbb{Z}_3$-symmetric Askey-Wilson
relations.
