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I'm doing a spherical electromagnetic motor and I need to design a main ball fully covered of circular holes (all of the same size) so I put the neodymium magnets inside them. The sphere is going to be made on a 3D printer.

I just started with Blender but I think I will manage to make the circular carving but I do not know how to make it all around the ball.

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You may do it by beveling the Ico Sphere and using the Solidify and Edge Split modifiers. enter image description here

Add an Ico Sphere with 3 subdivisions. enter image description here

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. enter image description here

Add Solidify Modifier and increase its Thickness value. Add the Subsurf Modifier below and give it some subdivisions. Apply the Solidify Modifier. enter image description here

Add the Edge Split Modifier above Subsurf and set its split angle to 80 degrees (you may experiment with value for optimal result though). enter image description here

Apply the modifiers and smooth the mesh in the Edit panel of the Tool Shelf (T). enter image description here

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).
enter image description here enter image description here

Now the holes have much more dense geometry, which I hope may let them create perfect circles after subdividing.

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    $\begingroup$ Yeah, good idea. Note, however, that these won't converge to perfect circles, in case that matters (e.g., if this is for a model to be 3D printed). $\endgroup$
    – wchargin
    Oct 19, 2016 at 19:35
  • $\begingroup$ Your question is about subdividing a square. In this case it's hexagon, wich creates almost perfect circle after subdividing. $\endgroup$
    – Paul Gonet
    Oct 19, 2016 at 20:12
  • $\begingroup$ Closer, yes, but still not precise. At twelve subdivisions of a unit hexagon, the maximum radius is 0.83333, the mean radius is 0.83155, and the minimum radius is 0.82994. After this many iterations, I would be surprised if this were a convergence issue. Of course, these tolerances of ~0.5% are unlikely to matter for most hobbyist parts. $\endgroup$
    – wchargin
    Oct 19, 2016 at 20:52
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    $\begingroup$ @wchargin Good point friend. I've added an edit to my answer, which shows another solution. Please check it out. $\endgroup$
    – Paul Gonet
    Oct 20, 2016 at 0:52

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