  There is a family of seventh-degree polynomials $H$ whose members possess the
symmetries of a simple group of order 168. This group has an elegant action on
the complex projective plane. Developing some of the action's rich algebraic
and geometric properties rewards us with a special map that also realizes the
168-fold symmetry. The map's dynamics provides the main tool in an algorithm
that solves "heptic" equations in $H$.
