You may do it by beveling the Ico Sphere and using the Solidify and Edge Split modifiers.
Add an Ico Sphere with 3 subdivisions.
Enable face selection mode, press A in Edit Mode to select the whole mesh. Now press Ctrl+B and drag the mouse outwards to bevel it. Select one of the hexagons, go to Select-->Select Similar-->Polygon Sides. Delete selected hexagons with X-->Only Faces.
Add Solidify Modifier and increase its Thickness value. Add the Subsurf Modifier below and give it some subdivisions. Apply the Solidify Modifier.
Add the Edge Split Modifier above Subsurf and set its split angle to 80 degrees (you may experiment with value for optimal result though).
Apply the modifiers and smooth the mesh in the Edit panel of the Tool Shelf (T).
EDIT: After @wchargin 's remark I experimented a bit and tried to solve it in another way.
Added an Ico Sphere with 3 subs, poked it with Alt+P and then beveled some vertices (Ctrl+B, V).
Now the holes have much more dense geometry, which I hope may let them create perfect circles after subdividing.