Some think that dialog is only between two people. But "dia" is a Greek prefix meaning "through" or "among".
Think of "diarrhea" , "dialysis" or "diabetes".
I prefer not to think of diarrhea, dialysis, or diabetes. How about diacritical, diagnosis, diagonal, diagram, diameter, diaphanous?
Some notable exceptions to the di- = two (diatomic) and the dia- = through, apart (diagnosis) are:
dial
diamond
diary
James, would you also prefer if three children splitting up a stash of goodies were said to "trivide" the spoils?
(I confess I have a similar peeve about the misuse of "between". The word has an Anglo-Saxon "two" right in the middle of it, for crying out loud!)
Dial and Diary are exceptions because they come from the Latin word for day and have no Greek DNA in them at all.