What kinds of dolphins live in the Antarctic or Arctic oceans?

Answer 1

There is no Antarctic Dolphin.

However, The hourglass dolphin Lagenorhynchus crucigerdoes occupy the Southern Ocean, and is rarely seen. The Southern Ocean is the most protein-rich ocean on earth, providing in its short food chain sufficient protein for all the animals live in these waters.

Answer 2

From its Wikipedia page:

"The hourglass dolphin (Lagenorhynchus cruciger) is a small dolphin in the family Delphinidae that inhabits Antarctic and sub-antarctic waters."

Note, however, that this animal is rarely seen.

Answer 3

The largest dolphin -- the Orca Whale -- can be found in both waters.