I wondered which spelling was correct after seeing each in writing.

Problem:
One of the three spellings is incorrect.

Explanation:
The compound noun “polka dot” — with a space in the middle — is an Americanism that dates back to the 1880s.

The word “polka-dot” — with a hyphen in the middle — is the adjectival form of this noun.

The word “polkadot” — with neither a hyphen nor a space in the middle — is not recognized in most dictionaries, although a search for this form (with the quotation marks) in Google returned about 2,090,000 matches.

In contrast, a search in Google for “polka dot” — with a space in the middle — returned about 9,300,000 matches.

I believe that the elimination of the space in more than two million Web instances is consistent with my “Devolution toward Simpler” linguistic hypothesis. It is simpler to omit the space than to include it.

Solution:
Use “polka dot” — with a space — as a noun. Use “polka-dot” — with a hyphen — as an adjective. Never use the no-space, no-hyphen form, which is a misspelling of the other two forms.