FTO: Bencisco and Nautilus

The FTO (face-turning octahedron) has eight triangular faces, each turning a third of a turn. Unlike a cube, its corners have more stickers and its triangle centres move independently. Recognition needs the whole triple and its neighbouring triangles, not just a face-colour outline.

Notation: U, F, R, L, D, B, BR and BL turn a face; Rw a face and the middle layer, Rs the middle layer alone, Ro the whole puzzle about R's axis, Rt, Lt and Ft the whole puzzle a quarter turn about a corner. Corner in front (CIF), the notation TNoodle and csTimer scramble in, holds U on top with the corner where U, L, F and R meet towards you; edge in front (EIF), the notation of the LowCubes sheets many of these algorithms come from, turns the puzzle until an edge of U faces you, so the same letter can name another face. The CIF/EIF switch on this page shows every algorithm and diagram in either. Cubemuch's sheets are translated into the same notation from their geometric move definitions, so every printed move and diagram uses the same convention. S and H are the tutorial's sledge and hedge:

Ben Streeter's Bencisco method builds a first block, completes the remaining centres, places the last bottom triple, then solves the last triples. Keep the block as an anchor while working on centres; finishing a centre too early can remove the slice needed to join the next triple. LBT references handle the last bottom triple when intuitive insertion becomes awkward.

Pair formation arranges the last triples into the next look's configuration. TL then LT splits the finish into a top-layer step and a triangle-centre step. TCP combines those finishes after pair formation; 1L3T finishes the complete last step. Pair-formation algorithms are not catalogued as distinct cases here: the existing goal cannot independently distinguish their starting cases. Do not mistake a short next-look finish for a complete L3T solution.

Nautilus builds a block, finishes centres, inserts the last triple, then treats the remaining layer as triangles and corners. It was developed by James Straughan, Liam Highducheck, Vincent Trang and Malte Ihlefeld, with community contributions. The key difference from the Bencisco finish is the last-layer organisation, not merely a different algorithm for the same final state.