mapping of cube by itself From exam textbook I am given to solve following problem: question is like  this
  in space how many lines  are such by which if turn  cube by $180^\circ$ it will map itself?   I was thinking   about this  problem many times I though  it should be axis of symmetry  for which answer would be  $4$ but in answers there is not 4  so I did not find solution of it  yet please help me to make it clear for me

What 4 did you get?  Clearly the axis has to pass through the center of the cube.  There are three through the face centers, six through the centers of edges, and four body diagonals.  You can see a figure here
