Taking BYU as a west team, they'd play the other two west teams every year so that would be the primary rivalry.

But they'd also play the teams from every other pod in at least 2 out of 3 years. And because they'd also mix in that 9th game, there'd be at least one in each of the other pods that they'd play in 5 consecutive seasons.

So in a 6 year span (ignoring any CCG appearances), you'd loosely play
2 teams 6x (those in your division)
6 teams 5x (those you meet up with in end-of-season showcase) - note that this depends on who you match up with. If it's the same team for two cycles, then you could end up taking two of these teams and making 1 a 6x and 1 a 4x.
3 teams 4x (those you never match up with in end-of-season showcase)

That's enough to build a strong rivalry with most of the teams (except maybe the ones that are never the same quality as you, which wouldn't be a rivalry anyway)