Admins are generally considered to have access everywhere so maybe best as promiscuous.
If the other groups need to connect to each other then they need to be in a community.
Infrastructure generally do, and you could say they are trusted so why not place them in a single community.
If you don't want students to connect directly, place them in an isolated. I'd trust teachers even less :) The method to share files should be by file server.
Don't forget, subnetting and access control. I wouldn't recommend placing all devices in a single subnet. depends on how many you have, but certainly a subnet for end users (teachers, students) and infrastructure would be a good idea.
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