LIT Visiting every cell, those with 3 exposed faces are corners (8), with 2 are edges (60), with 1 are faces (150), with 0 are interior (125). The formulas 8, 12×5, 6×25, and 5³ match the visit, and both sum to 7³.
AMBER The four names are the names of those counts.
WALL The partition is not a map of rooms beyond this grid.