OC: pairs and triples
Common
Every case cross-checked
Orient the remaining corners after edge orientation, using Grant's smaller orientation set.
3 adjacent corners - Rotate U/F/L, U/F/R, and U/L/BL C
(U) R U R' U R U2' R'
7 HTM · 6 algs
3 adjacent corners - Rotate U/F/L, U/F/R, and U/R/BR CC
(U2) R' U' R U' R' U2 R
7 HTM · 6 algs
3 non-adjacent corners - Rotate U/F/L, U/F/R, and U/BL/BR C
R U R' U2 R U2 R'
7 HTM · 6 algs
3 non-adjacent corners - Rotate U/F/L, U/L/BL, and U/R/BR CC
R U2 R' U' R U' R'
7 HTM · 6 algs
2 adjacent corners - Rotate U/F/L counterclockwise (CC) and U/F/R clockwise (C)
(U2') Dv2 R2' DR' R U2 R' DR R U2' R Uv2
9 HTM · 5 algs
2 adjacent corners - Rotate U/F/R C and U/R/BR CC
(U2) R BR BL' BR' R' BR BL BR'
8 HTM · 6 algs
2 non-adjacent corners - Rotate U/F/L CC and U/R/BR C
(U2) R' F R BR' R' F' R BR
8 HTM · 6 algs
2 non-adjacent corners - Rotate U/F/L C and U/R/BR CC
R U2 R' U R U2 R'
7 HTM · 6 algs
Source: Cubemuch, https://cubemuch.com/en/algs/megaminx/oc-two-three/, retrieved 2026-10-29: case names and groups, and each case's algorithms: those credited to the community sheets it cites first, in its order, then those its search found, best-scored first (no votes or setups). The source's first six verified alternatives per case are retained; further generated variants are omitted to keep case pages and the client bundle bounded. Every algorithm shown was checked by the logic engine; rejected ones are listed in docs/db-exclusions.md.