There are many test networks on Tezos.
What are the active and soon to be active public ones? How do we participate? Are there accessible public nodes?
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As commented above, https://tezos.gitlab.io/introduction/test_networks.html lists the current networks: mainnet, Edo2Net (mainnet test), Florencenet (next protocol, if it passes)
Every network is public and both test networks have free tokens from the faucet. You can participate by downloading/running the latest tezos software and using the
--network flag to specify the network to which you want to connect.