Learn · Level 3 · orientation
The 57 orientations
After the first two layers, the top face is a scatter of yellow. Fifty-seven patterns cover every scatter a legal cube can show, proved by enumeration of all 216 of them. One algorithm each, and the face turns solid yellow in one pass.
Nobody sits down and memorises all fifty-seven at once. Solvers collect them a few at a time over months, starting with the shapes they see most. Each tile is the top face seen from above: yellow where yellow already shows, dark where it doesn't, with ticks around the rim showing where each missing yellow points. The family names, the fish and the lightning bolts and the knight moves, are how cubers actually talk about them.
Start with the seven cross cases: their edges are already up, they include the Sune and Antisune from Level 2, and together they cover every solve where your yellow cross arrives free.
Dot
Square
Small lightning
Fish
Small lightning
Knight move
Dot
Cross
Corners done
Awkward
P shape
T shape
C shape
Fish
W shape
Fish
W shape
Big lightning
Awkward
P shape
T shape
C shape
L shape
I shape
L shape
I shape
Corners done
Checked by simulation before publishing: the position shown plus the moves shown must produce a finished cube, and the algorithm must touch nothing outside its own job. The diagram and the player are drawn from the same simulated position, so they cannot disagree. Completeness is checked by enumeration: the 57 definitions cover all 216 reachable orientations, each exactly once.