It makes most sense to design the schedule for 24 weeks, at which point it can be arranged that all players have had exactly 16 games, and 8 bye weeks, also it is possible to arrange that every player partners every other either 3 or 4 times, and every player opposes every other player either 6 or 7 times. Below rows correspond to weeks, and after each scheduled game the 2 players with a bye are shown in brackets.
(5 4 v 2 1) [3 6]
(6 5 v 3 2) [1 4]
(4 6 v 1 3) [2 5]
(5 2 v 1 6) [3 4]
(4 1 v 3 5) [2 6]
(6 3 v 2 4) [1 5]
(2 3 v 5 1) [4 6]
(1 6 v 4 2) [3 5]
(5 6 v 3 4) [1 2]
(1 2 v 4 3) [5 6]
(3 5 v 6 1) [2 4]
(4 5 v 2 6) [1 3]
(3 1 v 6 2) [4 5]
(6 4 v 1 5) [2 3]
(2 4 v 5 3) [1 6]
(2 6 v 4 1) [3 5]
(3 6 v 5 4) [1 2]
(2 1 v 5 3) [4 6]
(2 5 v 4 6) [1 3]
(1 3 v 4 2) [5 6]
(1 5 v 6 3) [2 4]
(3 4 v 5 2) [1 6]
(1 4 v 6 5) [2 3]
(3 2 v 6 1) [4 5]
(2 5 v 3 4) [1 6]
(1 4 v 3 6) [2 5]
Above I have added on two extra rounds to make it up to 26 weeks - of course as 26 is not a mulitple of 3, the number of sessions can not be balanced and so players 3 and 4 end up with one more game than the other 4 players. Hope that helps.
