(Secretariat of the Antarctic Treaty)
Antarctica does not have a constitution. The Antarctic Treaty of 1959 functions as the governing document for Antarctic affairs.

(U.S. Dept. of State)
The Status List is the official record of countries that have acceded to or ratified the Antarctic Treaty of 1959.

(U.S. Dept. of State)
"Note 2: Antarctica consists of the territory south of 60 degrees south latitude. This area includes claims by Argentina, Australia, Chile, France, New Zealand, Norway, and the United Kingdom, the legal status of which remains in suspense under the terms of the Antarctic Treaty of 1959. The United States recognizes no claims to Antarctica."