If you have a rotation axis (it should be where those green boxes meet at that point) then rotate all vertices of the box around that rotation axis with the right angle and you will have your new box.
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I asked a similar quesion previously, but it had assumptions which may not have been true.
The blue platforms are .2 high, and angled at 45 degrees away from each other. The bottom right of the grey cube is point 0,0,0. I want to rotate the grey cube 135 degrees so that it lands exactly on the other platform. Around what coordinates do i rotate the cube, and why?