I received the following from David Singmaster, forwarded with
permission.

I thought I remembered that antipodes is actually singular! In fact
it is singular in Greek but English recognizes both antipodes and antipode.
But the Antipodes means the region on the earth opposite to where one is and
is construed as a plural though its sense is singular. So antipodes is
actually not too bad a word for all the points which are maximally far away
and antipode should be reserved for the case where there is a unique
maximally distant point.

Prior to my first post on this subject, I consulted a mathematics
dictionary. This time, I consulted an English dictionary as well.
It indicates that "antipode" is a back formation from the Greek
"antipodes", and that the pronunciation is anglicized as "AN-ti-POHD".
There is a separate entry for "antipodes". (It seems unusual for a
dictionary to have a separate entry for a plural form.) The plural
pronunciation retains its Greek form as "an-TIP-uh-DEEZ".

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