Captain Dayton orders no shoes on the Solvang bridge's new carpet
A carpet was a flat, usually fixed, textile used as a large area floor covering.
Carpet color was considered part of a room's aesthetic design, often matching other aspects of the space or selected to accommodate the visual frequency range of the viewer. (VOY: "Human Error"; DS9: "Improbable Cause") Red carpet in particular used by some cultures to denote special treatment. (ENT: "Desert Crossing") They could be damaged, such as by burning or extensive use, or stained, and were periodically cleaned. (TNG: "Ship In A Bottle"; DS9: "Soldiers of the Empire"; VOY: "Unimatrix Zero")
In 2152, Captain Archer persuaded Commander Tucker to join him on a visit to the Torothan homeworld, saying that their host Zobral promised to "roll out the red carpet" and indulge his guests. (ENT: "Desert Crossing")
Carpet was also used in the guest quarters aboard Galaxy-class starships like in 2364 aboard the USS Enterprise-D. (TNG: "Conspiracy")
In 2369, a burn mark on a carpet was one of the pieces of evidence that Data, posing as Sherlock Holmes in the holodeck used to prove that a murder had been committed. (TNG: "Ship In A Bottle")
In 2370, shortly after borrowing Data's cat Spot Geordi La Forge complained that she coughed up hairballs all over his carpet. (TNG: "Force of Nature")
Later that same year, Doctor Julian Bashir requested special atmospheric specifications for the guest quarters of the Yalosian ambassador, a mixture of 60% nitrogen, 10% benzene and 30% hydrogen fluoride. A test of the mixture revealed it to be so corrosive that it dissolved the carpets when Major Kira Nerys tested it. Bashir's solution was to rip out the carpets, but warned Kira to not replace them with anything red or orange, as Yalosians could not see that part of the color spectrum. (DS9: "Improbable Cause")
In 2372, Jadzia Dax attempted to temper Worf's enthusiasm for the discovery of what he believed to be the Shroud of the Sword by saying the station could be carpeted with the many forgeries peddlers attempted to sell. (DS9: "The Sword of Kahless")
In 2373, Sorm vaporized Tauvid Rem in his guest quarters on Deep Space 9, leaving marks on the carpet. Odo later discovered the marks while looking for Tauvid Rem. (DS9: "A Simple Investigation")
Later that year, Julian Bashir sarcastically chastised General Martok for dripping blood on the carpet after treating his injury, noting that it takes days to get the stain out. (DS9: "Soldiers of the Empire")
In 2375, Bashir remarked that he hated the carpet that covered the bridge of the USS Defiant after the crew boarded the vessel for the first time. (DS9: "The Dogs of War")
Later the same year, Norvo Tigan noted his mother disapproved of suicide, as it would get blood on the carpets. (DS9: "Prodigal Daughter")
In 2377, shortly before Captain Janeway departed Voyager to infiltrate Tactical Cube 138, Chakotay asked if she wanted any carpets to be cleaned. (VOY: "Unimatrix Zero")
Later that same year, B'Elanna Torres sarcastically responded to Commander Kohlar's questioning where her images of Kahless and her family's crest were when he did not see them displayed in her quarters: "they clashed with the carpet." (VOY: "Prophecy")
In 2378, a hologram of Neelix advised Seven of Nine the drapes in her new quarters should match the carpet. (VOY: "Human Error")
In 2381, as part of a readiness drill, the crew of the USS Cerritos switched testing requirements for the high- and low-ranking officers. After each realized the other's duties were not as simple as they first assumed, Captain Carol Freeman observed to Ensign Beckett Mariner that "the carpet's always greyer on the other side of the ship." (LD: "I, Excretus")
Later that year, Ensign Beckett Mariner jokingly blamed Captain Carol Freeman for "wearing out that carpet" as she paced in her ready room in contemplation of a lecture she was about to deliver. (LD: "Grounded")
Later that same year, Nick Locarno told Ensign Beckett Mariner that the Nova One, which he'd designed himself, did not have Starfleet carpet or wooden paneling. (LD: "Old Friends, New Planets")
During her service on board the USS Cerritos, Lieutenant junior grade T'Lyn was assigned to escort a contingent of three Betazoid diplomats, one of which opined that Starfleet carpeting was perfect for passing out on. (LD: "Empathological Fallacies")
When the Klowahkan food critic Sir Legnog visited the USS Cerritos, he assumed they had never vacuumed the carpets. (LD: "A Farewell To Farms")
In 2382, after encountering a purple USS Enterprise-D, Ensign Beckett Mariner wondered if its carpets matched the hull. (LD: "Fully Dilated")
In 2401, upon returning to the bridge of the USS Enterprise-D 30 years after its loss at Veridian III, he commented to the other members of his former senior staff that the remembered the one thing he missed the most: "the carpet." (PIC: "Võx")