New Zealand is approximately antipodal to Britain, so no problem with the British using that term for that part of the world. But for Americans to call NZ the “Antipodes” is nonsense. The opposite side of the world from North America is way out in the Indian Ocean. Somewhere west of Australia and south of Indonesia where there’s no land at all (except some islands called Kerguelen Land, antipodal to Alberta, Canada).
The way to find the antipodal point from where you are is easy: Switch latitude N to S and keep the same number. The longitude switches from W to E, and the number is 180 minus your position.
All the Muslims around the world face Mecca when they pray. The antipodal point to Mecca is an island called Tematagi in the Tuamoto Archipelago in the South Pacific. The place that they all turn their backs on. This answers the question asked by the 17th-century Ottoman Turkish essayist Katip Çelebi if there is any spot on the globe where the direction of Mecca could be equally any direction at all. He figured out that it would be the antipodal point even though he didn’t know there really was an island called Tematagi there.
Circa 1970 Isaac Asimov wrote one of his essays about antipodal points. He concluded by noting that the antipodes of Vietnam was in Ecuador, so people fed up with the war could go there to get as far away from Vietnam as possible.