Hopefully it's possible to play 11 rounds, in which case a schedule exists where every player is matched against every other exactly twice.
(12 4 7) ( 1 2 6) ( 3 5 9) ( 8 10 11)
(12 5 8) ( 2 3 7) ( 4 6 10) ( 9 11 1)
(12 6 9) ( 3 4 8) ( 5 7 11) (10 1 2)
(12 7 10) ( 4 5 9) ( 6 8 1) (11 2 3)
(12 8 11) ( 5 6 10) ( 7 9 2) ( 1 3 4)
(12 9 1) ( 6 7 11) ( 8 10 3) ( 2 4 5)
(12 10 2) ( 7 8 1) ( 9 11 4) ( 3 5 6)
(12 11 3) ( 8 9 2) (10 1 5) ( 4 6 7)
(12 1 4) ( 9 10 3) (11 2 6) ( 5 7 8)
(12 2 5) (10 11 4) ( 1 3 7) ( 6 8 9)
(12 3 6) (11 1 5) ( 2 4 8) ( 7 9 10)
