The Octagon is a human facility located in Capitol City. It is in the process of being built since parts of the building are unfinished.
This is based off the Pentagon which monitors activities and military actions.
You will also go to the Octagon when Silhouette orders Armquist to meet with the Joint Chiefs of Staff in order to unite the Military. You will have to scan a Scientist to get into the base eventually. One will say the password is "Blue Rider". Once you get in, Silhouette and Armquist are meeting in front of the Octagon. After you listen to their conversation, you have to get back to your Saucer and go to Union Town to kill Armquist before he unites the Military against Crypto.