[Someone]

According to http://en.m.wikipedia.org/wiki/Quadripoint, there currently isn't any quadripoint between countries, although it is awfully close between Namibia, Botswana, Zambia and Zimbabwe.

Trijunctions are very common. Luxembourg has 3 of them, Germany (if I count correctly) 7.

[JadeNB]

Wow—regardless of its use to answer the question, that's a new word for me, and a fascinating article. (Who would have expected such a debate to lead to literal shots fired? Well, I guess any student of cartography and history, but not me.) Thanks!