plotting - Draw a triangulated sphere

How to draw a triangulated sphere such as the one below in Mathematica, without being restricted to these colors, but with a more uniform color (possibly with some shaded area), and with the background frame removed?

Answer

If you're a) on 10+ and b) don't need this cells to truly be colored, you can try this:

mesh = DiscretizeRegion@Sphere[];

MeshRegion[mesh,
 Lighting -> Sequence @@@ {
    ConstantArray[{"Point", Red, {0, 0, 75}}, 2],
    Map[{"Point", Yellow, Append[#, 0]} &,
     CirclePoints[3., 6]

     ],
    ConstantArray[{"Point", Blue, {0, 0, -75}}, 2]
    },
 MeshCellHighlight -> {{1, All} -> Black}

 ]

This is just tricking you into thinking it's colored using Lighting. I was too lazy to highlight each cell. It's possible to write code to color an arbitrary discretized surface at the cell level. I've done it, but it's more code than I want to post here and isn't thoroughly proof-read. If you need that I can dig it up from wherever it's hiding, though.

Update

OP mentions in the comments that he's really interested in the triangulation. That's easily extracted as such:

triangulation =
  With[{cds = MeshCoordinates@mesh},
   MeshCells[mesh, 2] /. i_Integer :> cds[[i]]
   ];

And just to check that we pulled it out right:

triangulation // Graphics3D