I am showing a SubDivisioned Planet down to 9 subdivisions.  I found the problem since Sub Division 0 looks like origami, but everything else looks fine.  If you notice towards the end, you can see the heights embedded in the points.  And best of all, no poles!

Note:  This is not all of it by any means.  I need to go down to subdivision 19, but I needed to get this running completely.  Unlike the original "sphere" you saw, this actually has height information in it and can drill down.