For a 6-cell row, only 14 arrangements are valid.

Two symmetries apply to every row: complement (swap ↔) and reversal (read right-to-left). Under both, the 14 rows collapse into 5 equivalence classes.

  1. ↔ {1, 14}

  2. ↔ {4, 11} (alternating)

  3. ↔ {6, 9}

  4. ↔ {2, 3, 12, 13}

  5. ↔ {5, 7, 8, 10}

Three classes (A, B, C) have size 2 (complement and reversal produce the same row). Two classes (D, E) have size 4 (complement and reversal produce four distinct rows).