06-09-2011, 04:33 PM
The tesseract can be unfolded into eight cubes, just as the cube can be unfolded into six squares (view animation). An unfolding of a polytope is called a net. There are 261 distinct nets of the tesseract. The unfoldings of the tesseract can be counted by mapping the nets to paired trees (a tree together with a perfect matching in its complement).