The Rubik's Cube,
as a Group

All edges flipped — one of three positions maximally far from solved

Every edge sits in its home slot, but all are flipped ($c_p=e,e_p=e,c_o=0,e_o=(1,1,\dots ,1)$). Solvable in exactly 20 HTM moves, and no fewer — the lower bound nailed down first when Rokicki et al. proved God's number = 20 in 2010.

U R2 F B R B2 R U2 L B2 R U' D' R2 F R' L B2 U2 F2