Just for completeness - if you really want to create a 3D-print, then you could continue like so:

gr = Plot3D[(x^2 - y^2)/25, {x, y} \[Element] reg, BoxRatios -> Automatic, PlotTheme -> "ThickSurface", 
   ImageSize -> Large, PlotPoints -> 30];
flower = RegionUnion[DiscretizeGraphics[gr], Region@Sphere[{0, 0, 0}, 1.5]]

Lanee Young,

here is one simple way:

(* complete flower as polar plot: *)
ppl = PolarPlot[.5 (7.89 + 8.12 Cos[4 t] + 8.526 Sin[4 t]^2), {t, 0, 2 Pi}];
(* as a little hack - destillation of points: *)
pts = Cases[ppl, Line[{pts__}] :> pts, All];
(* converting as a region: *)
reg = DiscretizeGraphics@Graphics[Polygon[pts]];
(* plot - suitable for 3D-printing: *)
Plot3D[(x^2 - y^2)/25, {x, y} \[Element] reg, BoxRatios -> Automatic, 
 PlotTheme -> "ThickSurface", ImageSize -> Large]