Fascism = totalitarianism + racial superiority complex.
Fascism is a system of government in which a dictator controls military, industry and commerce (and whatever other aspects of his nation that happens to become important to him), and takes tyrannical measures to maintain his control. Racism is often used as a tool, but is not necessarily a required quality for something to be "fascist". Fascist regime is necessarily Totalitarian, but a Totalitarian regime is not necessarily Fascist. Therefore, your formula should read:
Fascism = totalitarianism + dictatorship
Now, a Communist system is not necessarily Totalitarian, but Totalitarianism becomes the method of choice for maintaining Communism when a meaningful portion of the population does not wish to be under Communist rule. I suppose there may be some other way to enforce Communism on a large scale, but I don't know what that might be.