A T-hexomino is depicted below:

+--+--+--+--+--+
|  |  |  |  |  |
+--+--+--+--+--+
      |  |
      +--+

Prove that this hexomino cannot tile any size rectangle.

Consider its 3-D counterpart. Show that 25 of them can pack a 5x5x6 box.