  The requirement for solving a polynomial is a means of breaking its symmetry,
which in the case of the quintic, is that of the symmetric group S_5. Induced
by its five-dimensional linear permutation representation is a
three-dimensional projective action. A mapping of complex projective 3-space
with this S_5 symmetry can provide the requisite symmetry-breaking tool.
  The article describes some of the S_5 geometry in CP^3 as well as several
maps with particularly elegant geometric and dynamical properties. Using a
rational map in degree six, it culminates with an explicit algorithm for
solving a general quintic. In contrast to the Doyle-McMullen procedure - three
1-dimensional iterations, the present solution employs one 3-dimensional
iteration.
