Try this mental experiment.
1) Close your eyes and create a mental image of a cube.
2) Rotate the mental cube until you are familiar with all six faces.
3) Visualize a cube extending from each of the six faces.
4) Rotate this object mentally until you are familiar with each of the seven cubes.
5) Mentally place a black spot on one of the faces of the interior cube.
6) Move the black spot about noticing how its face is shared with one of the outer cubes.
7) Visualize a black spot on one of the faces of one of the exterior cubes.
8) Visualize a black spot on the face of another of the exterior cubes that is orthogonal to the previous face.
9) Mentally move these spots around such that one mimics the movement of the other.
10) Mentally bring the spots together until they are coincident, so that the faces of the two cubes join into a single surface.
11) Merge the shared outer vertices of the two cubes containing the moving spot all the while keeping the shapes cubical.
12) Do the same with the remaining faces of the exterior cubes.
Latest Answers