There are as many dimensions as your imagination can stand. An infinite number. But you may not be able to experience them directly. As far as space and time, where we live, physicists generally think of the three space dimensions as you list them with the fourth dimension being time. The thing about time is it only goes one way: into the future. The other dimensions are two way. After the fourth dimension there can be as many as you like. Mathematicians and physicists use these higher dimensions for lots of things like network theory, black holes, and much, much more.
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