To play ordinary 2D tetris well, you have to learn to recognize chiral variants (such as the ones below) from one another.
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You
can't simply match them up by rotating them in the plane. However, in existing 3D tetris (such as BlockOut) you can easily substitute one with another by rotating this shape through the 3rd dimension.
Unfortunately, there are also chiral 3D shapes that cannot be matched up against each other by rotating them in 3-dimensional space (e.g., left screw tetracube / right screw tetracube), but can be matched by rotating them through the 4th dimension.
Fortunately, we have tools to do that: mirrors, and hence the idea:
A 3D tetris, with mirror side walls. By pushing your brick onwards to the wall, you obtain a mirror image of the brick from the alternate virtual reality, and you're in business.