Floppy Cube turning - i.e. an edge piece may only twist if there is at least one corner piece adjacent to it. The mass-produced version does not feature this mechanism, which allows edge pieces to twist "on their own" - causing the puzzle to be considerably easier. The four edge pieces now have 4 orientations each on the Super Floppy Cube (compared to the Floppy Cube's 2); therefore, the edges can now be orientated in 4 different ways. However, the edges still cannot be permutated. There are now 12 different locations that the four corner pieces could be located in (up from
Partial cube "Hamming labeling"; it represents an isometric embedding of the partial cube into a hypercube. was the first to study isometric embeddings of graphs into hypercubes. The graphs that admit such embeddings were characterized by and , and were later named partial cubes. A separate line of research on the same structures, in the terminology of families of sets rather than of hypercube labelings of graphs, was followed by and , among others. Every tree is a partial cube. For, suppose that a tree "T" has "m" edges, and number these edges (arbitrarily) from 0 to "m" − 1. Choose a