In using sum contrast coding, let's say you have 6 levels to a factor, you still end up with a table of results with (level - 1) dummy codings, e.g. x1, x2, x3, x4, x5. Yet, if the intercept is now an unweighted mean (and not a reference level), why do you not have 6 levels?

Sorry if I'm missing something obvious here. My brain is trying to work today.