polynominal is a subtype of nominal. A nominal value may be either polynominal or binominal, the first meaning there are more than 2 distinct values, the latter one meaning there are exactly two values. Hence, a polynominal value is always a nominal one, but this is not true the other way round.
principally, yes. On the other hand, there is currently no operator available who distinguishes between nominal and polynominal. From an algorithmic point of view, if an operator supports more than two values it also supports two as well. Hence, in most places you will not find any distinction between polynominal and nominal.
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Polynominal and nominal are identical in the current implementation, so they are interchangeable. In fact the nominal type could be hidden from the users, but for historical reasons it is not. Binominal is different in that a binominal attribute can have at most 2 different values.