Here is how to create these graphics within Mathematica:

<<Graphics`Shapes`

<<Graphics`Polyhedra`

g = Show[Graphics3D[{
    RotateShape[First[Polyhedron[Cube]],Pi/4.,0,0],
    RotateShape[First[Polyhedron[Cube]],0,Pi/4.,0],
    RotateShape[First[Polyhedron[Cube]],Pi/4,Pi/2,0]
}]];

This is already everything you need to produce the topmost picture, if you stay in Mathematica. The procedure to display the Graphics3D object with LiveGraphics3D is explained in the documentation.

In order to get rid of intersecting polygons we have to construct all the polygons which are effectively visible, here is my solution:

e=2;
h=(Sqrt[2 e^2]-e)/2;
c=e/2-h;
t0={0,0,e/2+h};
t1={e/2,0,e/2+h};
t2={0,e/2,e/2+h};
f1={e/2,-h,e/2};
f2={e/2,+h,e/2};
f3={+h,e/2,e/2};
f4={h,h,e/2};
b1={e/2-c/2,e/2-c/2,e/2-c/2};

atom=N[{Polygon[{t0,t1,f2,f4}],Polygon[{t0,f4,f3,t2}],Polygon[{t1,f1,f2}],
      Polygon[{f2,f3,f4}],Polygon[{f2,b1,f3}]}];

face={atom, RotateShape[atom,Pi/2,0,0],RotateShape[atom,2Pi/2,0,0],
    RotateShape[atom,3Pi/2,0,0]};

tripleCube={face,RotateShape[face,0,Pi/2,0],RotateShape[face,0,2Pi/2,0],
    RotateShape[face,0,3Pi/2,0],RotateShape[face,0,Pi/2,Pi/2],
    RotateShape[face,0,Pi/2,3Pi/2]};

g=Show[Graphics3D[{
      FaceForm[SurfaceColor[GrayLevel[1]],SurfaceColor[Hue[0.6,1,1]]],
      tripleCube},{Background->RGBColor[1,1,1],
      LightSources ->
         {{{1, 1, 1}, GrayLevel[1]}, {{-1, -1, -1}, GrayLevel[0.5]}}, 
      AmbientLight -> GrayLevel[0.2], Boxed -> False}]];