The Flag of Apartment 4A
The official flag of Sheldon and Leonard's apartment is a gold lion rampant on a field of azure. The flag was first introduced in "The Staircase Implementation" in a flashback to Leonard first applying to become Sheldon's roommate. According to Sheldon, the flag must only be flown upside down when the apartment is in distress.
A magnet version of the flag is kept on the refrigerator and has been turned upside down in times of distress. A full-sized flag is show opposite the American flag in the background of Sheldon's vodcast "Fun with Flags". When Raj temporarily moved into the apartment in "The Roommate Transmogrification", he was given a lapel flag by Sheldon.
The official flag of Apartment 4A is flown behind Sheldon during episodes of Fun with Flags, alongside the American flag.
Featured in these episodes:
In a flashback to Sheldon interviewing Leonard to be his next roommate, he introduces Leonard to the official flag of the apartment: a gold lion rampant on a field of azure. Sheldon says the flag only flies upside down when the apartment is in distress.
In another flashback to Leonard experimenting with rocket fuel in the apartment, Sheldon turns the flag upside down when Howard's rocket fuel is about to explode.
When Raj starts staying in Leonard's room because Leonard and Priya are staying in his apartment, Sheldon gives Raj a lapel pin version of the apartment flag, which "Leonard was too cool to wear."
The apartment flag, a gold lion rampant on a field of azure, is one of two flags (the other being the U.S. flag) shown in the background of Sheldon's vodcast, "Fun with Flags", which he started in the episode.