These single-hex extenders increase the Galaxy Frame from a 3-ring layout to a 4-ring layout, allowing you to play Twilight Imperium 4th Edition with 7-8 players with the Prophecy of Kings expansion.
These are also needed for building a smaller 2-ring galaxy, which is really fun for a 3-player game.
Additional extender sets can be added to create a 5-ring galaxy, or create asymmetrically long or wide galaxies.
Each set comes with 6 extenders.