Before you worry about 'nor' or a comma, you'll have to re-think what you are trying to say. If you sit next to someone, you sit on their left or right. It makes no sense to speak of sitting horizontally, vertically or diagonally next to someone.
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fivejedjonIt makes no sense to speak of sitting horizontally, vertically or diagonally next to someone.Have you ever been watching a football match? If so, then you might have been able to see how spectators are seated there.
AnonymousI feel that the underlined part should be "either vertically, horizontally, or diagonally" since the clause before it has the word "never," which makes it negative in meaning.You can do that. Yes. That's probably how I'd say it.
AnonymousAnd there should be another "nor " before "horizontally.'It's not necessary