All of the lower 48 states of the US, and most of Canada, is in the Indian Ocean.
All of Australia is in the north Atlantic Ocean.
Practically all of Africa and Europe in in the Pacific Ocean. (The main exception is part of Spain which is antipodeal to New Zealand).
There’s a lot of water on the surface of the world: the main area where land is antipodeal to land is South America and East Asia, e.g., most of Argentina is opposite China.
A lot of you seem to to forget that if you live in the northern hemisphere, you come out in the southern hemisphere (and vice versa).
So…
Your latitude switches from N->S or S->N
Your longitude rotates 180 degrees. If you live in the Western Hemisphere, treat your longitude as a negative number and add 180. If you live in the Eastern hemisphere, subtract 180, the result being a West Longitude.
That antipodal map is absolutely correct.
You must also move your lattitude by 180[sup]o[/sup]. Suppose you are at the equator at some location. If you go straight through the earth you will end up at the equator on the opposite side of the earth. since you can’t go straight through you can get to the same location by going up a line of longitude to the north pole and then down the corresponding longitude to the equator after having gone half way around the earth. If you at 10[sup]o[/sup]N you will end up at 10[sup]o[/sup]S also by going up to the north pole, or down to the south, and then down, or up, to -10. 10 pairs with -10, 20 pairs with -20, and n pairs with -n.
By the way, can I claim an SDMB record for “shortest time between visiting two precisely antipodal points”? I didn’t realise it until later, but I travelled around the North Island of New Zealand in February 2003, and then visited Andalucia in southern Spain in July the same year. By my reckoning, when I was in Spain, en route to Ronda, I must have passed a point exactly “opposite” somewhere on the Coromandel peninsula, where I’d been just 5 months earlier…