Chaotic attractors with the symmetry of the dodecahedron

Polynomial functions in three space that are equivariant with respect to th e symmetries of a dodecahedron are determined. These are constructed with a sum of functions under changes of coordinates with respect to the group. M onte Carlo searches through parameter space lead to functions that are expe rimentally chaotic and that have visually appealing attractors. Ray-tracing techniques enable the rendering of the three-dimensional attractors so tha t both their complexity and symmetry can be observed.