Te namesake and capital of the Hyperiad Empire is the Hyperion System, revolving around the remains of the main sequence star, Hyperion.
Before the founding of the Hyperiad Empire, the Hyperion star system was the capitol of the Titanic Hegemony, the ruling body of mankind. During the Astromachy, the Promethean Emperor waged a war against the Titanic Hegemony that spanned across the galaxy and culminated in the Hyperion Nova, when the Promethean Emperor forced the sun of the Hyperion star system to go Super Nova and then rapidly collapse in on itself forming a black hole. Most of the remaining Hegemony forces, as well as the majority of the remaining Titan, were dragged into the gravitational pull of the remains of the Hyperion sun, ending the Astromachy.
After stabilizing the remaining black hole, the Promethean Empire decided to establish his capitol in the remains of the Hyperion system, constructing several artificial satellites to orbit the gravitational singularity at the center of the system.