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The Forum was an ancient human structure located in the City of the Gods, on ancient Kobol.
After the exodus from Kobol and the establishment of the Twelve Colonies, a second Forum was built on Caprica, either in Delphi or Caprica City.
It is not clear if the Forum was religious in nature (perhaps a temple to the Lords of Kobol), governmental, or simply a civic gathering place. Laura Roslin describes it as a large dome-like structure with a colonnade of pillars surrounding it (TRS: "Kobol's Last Gleaming, Part I").
Other structures on Kobol that might be mirrored on Caprica include the Opera House and the Temple.