I would like to set a scene inside a box, such that its faces will consist of
grid lines and will be transparent. That is, if the camera is INSIDE the box, it
will see something which is outside and vice versa.

This is the best I could get:

//-----------

#include "textures.inc"
camera {
 perspective
 location < 4.0, 4.0, 12>
 right x * 1
 up y * 3/4
 angle 60
 look_at < 0.0, 0.0, 0.0>
}

light_source {
 < 0.0, 100, 100>
 rgb <0.999962, 1.000000, 1.000000>
}

box {
 < -2, -2, -2>, <2,2,2>
// no_shadow
 hollow on
// pigment {
//  rgb <0.000000, 0.202852, 1.000000>
// }
 pigment {
        Tiles_Ptrn()
        color_map{
         [0.02 color rgb <1,1,1>]   // white stanchions
  [0.04 color rgbt <0,0,0,1>]  // black spaces
        }
        rotate z*90  // rotates the pattern onto the "upper side" of the plane
 }
}

sphere {
 <0.0, 0.0, 0.0>, 0.5
 material {
  texture {
   pigment {
    rgb <0.000000, 0.202852, 1.000000>
   }
   normal {
    brick 0.5 //amount
   }
   finish {
    diffuse 0.6
    brilliance 1.0
   }
  }
 }
}
//--------

How can I finish it?

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