Our objective is encoding of local protein structure.
And to encode the shape of ...
As an example, let's consider the alpha-helix of length 13 shown in the middle figure.
By simple folding, we obtain the red object of 85 tetrahedron tiles shown on the left. But the object is more complicated than the original alpha-helix.
On the other hand, if we permit translation and rotation, we would obtain the object of 13 tetrahedron tiles shown on the right. And it will turn out that we could capture the local features of proteins by the discontinuous tetrahedron sequence.
The following slides illustrate the coding algorithm briefly.