The Red Star was an arcology, a massive architectural residence located in Red Square in Moscow during the 23rd century.
History and specifics[]
In the 2250s, Pavel Chekov visited Red Star and went to its top floor during his first semester at V.I. Lenin Exceptional School. At nearly 1,000 feet tall, Chekov described it in his diary as the largest archeological structure on Earth. (TOS reference: Star Trek II Biographies)
In 2277, while under the influence of an illusion-generating machine, Chekov saw Red Star along with three nearby arcologies Kalilingrad, Leningorá, and Spirit of Tomorrow. (TOS - Plot-Your-Own Adventure Stories novella: Distress Call!)