Featured Map: Useless Loop: How Many "Farthest" Hops? (25 January 2011)

Each airport information page on the Great Circle Mapper includes information about the airport which is farthest away—the airport closest to the antipode of the one being viewed. For example, the farthest airport from Useless Loop, Australia is Grand Turk International in the Turks and Caicos Islands:

Farthest:

GDT: 12004 mi / 19319 km Grand Turk [J.A.G.S. McCartney Intl (Grand Turk Intl)], Grand Turk Island, TC

The farthest airport from Grand Turk is not Useless Loop, however, but is Exmouth Gulf, Australia. Many people enjoy a game wherein they keep following the link until the path start to repeat. For example, starting from Useless Loop, there are five "farthest" hops before the cycle loops back to the preceeding airport:

from Useless Loop, WA, AU
(1) to Grand Turk International, TC
(2) to Exmouth Gulf, WA, AU
(3) to San Juan [Fernando Luis Ribas Dominicci Airport], PR, US
(4) to Barrow Island, WA, AU
(5) to The Settledment, Anegada, VG
then back to Barrow Island

This is best viewed using an azimuthal equidistant projection, centered on the starting point:

Can you find a longer cycle? Where does it start and how many hops does it involve?