I have 24 teams that will rotate to 12 stations (2 teams per station) Teams will not compete against another team more than once.
I got this trick from https://en.wikipedia.org/wiki/Edge_coloring#Examples.
Number the teams 1 to 24. Arrange teams 1 to 23 evenly spaced on the circumference of a circle, and place team 24 in the center.
On the $i$th round, for $i$ = 1, 2, ..., 23, have team 24 play against team $i$. For the other teams, divide them into pairs so that in each pair, the line connecting the two teams is perpendicular to the line connecting team $i$ to team 24. This means that team i – 1 plays i + 1, team i – 2 plays i + 2, and so on, where addition is modulo 23.