Mathematica RegionPlot on the surface of the unit sphere?

Question

I am using RegionPlot3D in Mathematica to visualise some inequalities. As the inequalities are homogeneous in the coordinates they are uniquely determined by their

Answer 1

SphericalPlot3D[0.6, {\[Phi], 0, \[Pi]}, {\[Theta], 0, 2 \[Pi]}, 
 RegionFunction -> 
  Function[{x, y, z}, 
   PolyhedronData["Cube", "RegionFunction"][x, y, z]], Mesh -> False, 
 PlotStyle -> {Orange, Opacity[0.9]}]