The term "long dozen" refers to the number thirteen. It is a way of counting that adds one more to the standard dozen, which is twelve.
In more advanced contexts, "long dozen" might be used humorously or in literature to refer to the idea of something being in excess or more than expected.
There are no direct variants of "long dozen," but you might see it in phrases like "long dozen eggs" meaning thirteen eggs instead of just twelve.
There are no idioms or phrasal verbs directly associated with "long dozen." However, you might hear phrases like "a baker's dozen," which means thirteen items (often used in baking).
"Long dozen" is simply a fun way to say thirteen. It combines the idea of a dozen (twelve) with one extra, making it a total of thirteen.