• DisplayFunction do the jobs.
• Using the example by @Simon Woods

RegionPlot3D[
 Mod[phi, Pi/3] < Pi/6, {r, 2, 3}, {theta, 1, Pi}, {phi, 0, 2 Pi}, 
 DisplayFunction -> 
  ReplaceAll[{r_Real, theta_Real, phi_Real} :> 
    r {Sin[theta]*Cos[phi], Sin[theta]*Sin[phi], Cos[theta]}], 
 Boxed -> False, NormalsFunction -> None, PlotPoints -> 60, 
 MaxRecursion -> 2, BoxRatios -> Automatic, PlotRange -> All, 
 Boxed -> False, Axes -> False]