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The generic second level tetraflexagon has twelve faces, and is still quite easy to fold up from a previously prepared strip of paper.
Figure 28:
Since each edge of the first level tetraflexagon spawns two new vertices, the full second level tetraflexagon has 12 vertices.

Figure 29:
Permutation of the squares along the strip for a normal second level tetraflexagon. They run in order, subject to packages being flipped over.

Figure 30:
Strips from which the second level tetraflexagon can be folded. One strip folds into a single sector, so two are needed altogether.

Figure 31:
Back side of the two strips for the second level normal tetraflexagon. One sector per strip.

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