Economic system doesn't really map to political system. The US, China, Nazi Germany are all capitalist, though the political systems are different. I guess the USSR would be an imperfect example of communism (everything owned/operated by the state, though not by the commune) but it didn't last.
I have to object to this usian definition of communism as "ownership by the state". That's just horribly wrong, I have no idea where they teach such crap.
Communism implies ownership by the
people, which is a different beast entirely*. Also the wealth distribution "from everyone according to their ability, to everyone according to their needs." It quickly becomes clear that communal species are, surprise surprise, as close to the commuist ideal as you can come.
* Yah. The real reason why communism doesn't work is literally because people aren't ants. The "owned by everyone" becomes "cared about by no-one" and "according to their needs" morphs to "some animals are more equal than others."