Omegahedron and the Alphahedron are the source of power for the entire city. The device can manipulate matter at a molecular level. The Omegahedron seems to have the power to create life, but it only creates the appearance of life, as Zaltar stated it's a "fancy shadow of the real thing." To less advanced races the technology it is indistinguishable from magic.
When Kara Zor-El's mentor Zaltar allowed her unauthorized use of the city's power source the Omegahedron as something she could experiment with, Kara lost control of it and it fell to Earth, falling into the hands of a power-hungry witch named Selena. Kara used a binary chute to travel to Earth, appearing as Supergirl in order to track down the Omegahedron. Kara eventually crossed paths with Selena, who was already using the power of the Omegahedron to build herself a fortress from which she could control the world. Selena cast Kara into the Phantom Zone, from which no Kryptonian could ever break free. However, Kara found Zaltar, who had been sentenced to the Phantom Zone for stealing the Omegahedron, and who risked his life to help the young Kryptonian break free from the Zone. Kara returned to Earth to battle Selena and ultimately succeeded in defeating her, retrieving the Omegahedron and bringing it back to Argo City.
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