[mg85089] Filled Polar plots

[Yaroslav Bulatov <yaroslavvb at gmail.com>]

What is the recommended way of creating filled polar plots? (assuming
it forms a closed non-intersecting curve)

I'm looking to create something like the image on http://en.wikipedia.org/wiki/Superformula,
but PolarPlot doesn't seem to have Filling options

formula[m_, n1_, n2_, n3_] =
  Function[{x}, (Cos[(m x)/4]^n2 + Sin[(m x)/4]^n3)^(-1/n1)];
vals = {{3, 5, 18, 18}, {2, 1, 4, 8}, {3, 3, 14, 2}, {7, 2, 8, 4}};
Table[PolarPlot[(formula @@ v)[x], {x, -Pi, Pi}, PlotRange -> All,
   Axes -> None], {v, vals}] // GraphicsColumn