  A machine-generated list of 192 local solutions of the Heun equation is
given. They are analogous to Kummer's 24 solutions of the Gauss hypergeometric
equation, since the two equations are canonical Fuchsian differential equations
on the Riemann sphere with four and three singular points, respectively.
Tabulation is facilitated by the identification of the automorphism group of
the equation with n singular points as the Coxeter group D_n. Each of the 192
expressions is labeled by an element of D_4. Of the 192, 24 are equivalent
expressions for the local Heun function Hl, and it is shown that the resulting
order-24 group of transformations of Hl is isomorphic to the symmetric group
S_4. The isomorphism encodes each transformation as a permutation of an
abstract four-element set, not identical to the set of singular points.
