7
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How do I draw a box with six cylindrical holes, one at the center of each face?

The code for the box:

pts = {{-0.5, -0.5, -0.5}, {-0.5, 0.5, -0.5}, {-0.5, 0.5, 
    0.5}, {-0.5, -0.5, 0.5}, {0.5, -0.5, -0.5}, {0.5, 
    0.5, -0.5}, {0.5, 0.5, 0.5}, {0.5, -0.5, 0.5}};
pts3 = ScalingTransform[{6, 6, 6}][pts];
pts4 = ScalingTransform[{7, 7, 7}][pts];
hex = {{2, 3, 4, 1}, {1, 4, 8, 5}, {4, 3, 7, 8}, {3, 2, 6, 7}, {2, 1, 
    5, 6}, {5, 8, 7, 6}};
box = BoundaryMeshRegion[Join[pts3, pts4], Polygon[hex], 
   Polygon[hex + 8], MeshCellStyle -> Opacity[0.2]]

Mathematica graphics

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9
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RegionPlot3D[
 RegionDifference[Cuboid[], 
  RegionUnion[Cylinder[{{0, .5, .5}, {1, .5, .5}}, 1/8],
              Cylinder[{{.5, 0, .5}, {.5, 1, .5}}, 1/8], 
              Cylinder[{{.5, .5, 0}, {.5, .5, 1}}, 1/8]]],
 PlotPoints -> 200,
 PlotStyle -> Opacity[0.7],
 Boxed -> False
 ]

or... just a bit crisper:

RegionPlot3D[
 RegionDifference[Cuboid[], 
    RegionUnion[
    Cylinder[#, 1/8] & /@ 
    {{{0, .5, .5}, {1, .5, .5}}, 
     {{.5, 0, .5}, {.5, 1, .5}}, 
     {{.5, .5, 0}, {.5, .5, 1}}}]],
 PlotPoints -> 200,
 PlotStyle -> Opacity[0.7],
 Boxed -> False]

enter image description here

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11
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RegionPlot3D[x^2 + y^2 > 1/16 && x^2 + z^2 > 1/16 && y^2 + z^2 > 1/16,
 {x, -1, 1}, {y, -1, 1}, {z, -1, 1},
 Mesh -> None, Boxed -> False, Axes -> False, 
 PlotStyle -> Opacity[0.8],
 PlotPoints -> 50
 ]

or

BoundaryDiscretizeRegion[
 ImplicitRegion[
  x^2 + y^2 > 1/16 && x^2 + z^2 > 1/16 && y^2 + z^2 > 1/16,
  {{x, -1, 1}, {y, -1, 1}, {z, -1, 1}}
  ],
 MaxCellMeasure -> 0.001, BaseStyle -> Opacity[0.8]
 ]

enter image description here

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