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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.
Since each edge of the first level tetraflexagon spawns two new vertices, the full second level tetraflexagon has 12 vertices.
Permutation of the squares along the strip for a normal second level tetraflexagon. They run in order, subject to packages being flipped over.
Strips from which the second level tetraflexagon can be folded. One strip folds into a single sector, so two are needed altogether.
Back side of the two strips for the second level normal tetraflexagon. One sector per strip.