Square-1: the Vandenbergh method

The Square-1 changes shape as it turns: each layer is a ring of edges and corners (a corner as wide as a pair of edges), and a slice turn swaps half of the top layer with half of the bottom. The Vandenbergh method first restores the cube shape, then sorts each layer's corners and edges (orientation), then puts them in place (permutation), fixing a parity if it is left.

Notation (WCA): (a,b) turns the top a twelfths of a turn clockwise seen from above and the bottom b clockwise seen from below; / turns the right half a half turn. A / is only possible when no corner straddles the cut; the engine refuses any other.