Hyperbolic Spinning Cube

frame[n_] := Graphics3D[
  {Thick, Red, Line[{{-2, -2, -2}, {2, 2, 2}}], Opacity[0.1], White,
   Table[Rotate[
      Cuboid[{-1, -1, -1}, {1, 1, 1}], \[Theta] + 2 Pi n /30, {1, 1,
       1}, {-1, -1, -1}], {\[Theta], 0, 2 Pi, 2 Pi/32}][[;; n]]}
  , Lighting -> "Neutral", Boxed -> False, PlotRange -> 2,
  ViewPoint -> {0, -5, 10}, ImageSize -> {300, 300}]