Skwuction

The Skwuction method is a reductionesque speedsolving method for the Square1 puzzle. It was originally created by Jaap Scherphuis, and greatly contributed to by Cary Huang. The name "skwuction" is a wordplay on Square1 and reduction.
Contents
The steps
 1. Turn the Puzzle into a cubic shape.
 2. Connect 8(all) corneredge pairs.
 2a. Solve 3 pairs intuitively.
 2b. Use an algorithm to solve the last 5 pairs.
 3. Solve the puzzle like a 2x2x2, using slice moves and 90180° layer turns.
 3a. Put the pieces in their correct layer.
 3b. Permute both layers.
Trivia
A note from Cary Huang is as following:
"For a time, I thought this method would work for speedsolving. I though sub15 was definitely possible. However, I hadn't really considered how difficult the recognition for last5edgepairing would be, and I think that's the major drawback. However, it's kind of similar to 4x4 edge pairing, in that you don't care where the pieces actually are, just whether they're paired up with similar pieces. And to many people, including myself, 4x4 edge pairing is actually really fun. It's fast, and recognition isn't hard at all. So maybe Sq1 edge pairing just needs some getting used to? Well, anyway, I gave up pursuing this method once I was averaging 26, and I haven't speedsolved a Square1 since then. I can't decide if it's worth it to start doing it again. I mean, in terms of just spamming algs to solve the thing, Skwuction just can't compare to the simplicity of the Vandenbergh method. (Although... if I recall correctly, Skwuction actually has a lower average movecount if you do it right.)"