impossible has 4 distinct synonyms spread across 2 of its 4 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its one recorded opposite is possible.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
not capable of occurring or being accomplished or dealt with
“an impossible dream”
totally unlikely
(used of persons or their behavior) not acceptable or reasonable
“impossible behavior”
something that cannot be done
“his assignment verged on the impossible”
Synonyms, antonyms and the broader and narrower relations for impossible come from Princeton University’s WordNet. Full sources and licences.