Are There Any Precise Definitions of Democracy, Republicanism, and Communism?

If you know, please tell me with numerical analysis. Democracy seems to be closer to republicanism than communism, republicanism seems to be closer to democracy than communism, and communism seems to be closer to democracy than republicanism.

Many definitions of communism seem to be contradictory, such as no social class distinction yet a centrally planned economy. What are a few of the many other contradictions with communism?