# Draw an arbitrary convex polyhedron [duplicate]

I want to draw a set of convex polyhedrons whose vertices are defined by spherical coordinates on the surface of a unit sphere.

How can I accomplish this in Mathematica?

It seems I cannot do it with PolyhedronData (even though the polyhedrons I want to draw are symmetric and quite simple). It even cannot draw a hexagonal dipyramid, {"Dipyramid", 5} works, {"Dipyramid", 6} does not.

I also tryed to use Polygon, but it leaves a number of faces not filled.