Possible brackets for 8 teams?

[Guest]

Hi, I am pondering about this series of problems and I am sure there is a systematic way of approaching it but I cannot seem to figure out. So the first problem is, if there are 8 teams, labeling team 1 to team 8, playing in a bracket (4 matches total), is there a way of listing out all unique brackets without duplication (i.e, team 1 vs team 8 in one bracket and team 8 vs team 1 in another bracket would be a duplication). I can only haphazardly figure out 5 brackets though I am sure I missed a duplication somewhere. Many thanks for helping me figuring this out

The number represents the team, i.e., 1vs5 means team 1 vs team 5

bracket 1
1vs5
2vs6
3vs7
4vs8


bracket 2
1vs2
3vs4
5vs6
7vs8

bracket 3
1vs3
2vs4
5vs7
6vs8

bracket 4
1vs6
2vs7
3vs8
4vs5


bracket 5
1vs7
2vs8
3vs5
4vs6