Vulcan IDIC
The Vulcan IDIC is an abbreviation for Infinite Diversity in Infinite Combinations, the name of a prestigious Vulcan award of merit, celebrating the vast array of variables in the universe -- the sea of possibility that a Vulcan-trained mind can navigate. In the Vulcan language, the term for IDIC is Kol-Ut-Shan. (VOY: "Gravity")
In 2154, T'Les smuggled a holographic map to her daughter T'Pol inside an IDIC medallion pendant. (ENT: "The Forge")
On formal occasions, Spock wore his IDIC medallion (in pin form) as part of his dress uniform. During a dinner function aboard the Enterprise, Dr. Miranda Jones had noticed Spock's Vulcan IDIC pin on his dress uniform. She inquired if it was to serve as a reminder to Jones that as a Vulcan, Spock can mind-link with the Medusans far better than she could. Spock noted, on the contrary, that he donned it to honor Dr. Jones and her achievements. (TOS: "Is There in Truth No Beauty?")
Solok sporting Logicians teamwear.
Vulcan IDIC pins were considered collectible merchandise in the retail markets of the 24th Century, not easily acquired in the Bajor sector. In late 2370, Quark listed Vulcan IDIC pins as plausible items that he could sell over the monitors on board of Deep Space 9 if given permission by Commander Benjamin Sisko. Including IDIC pins, other collectibles Quark listed that he could sell at a significant discount included Andorian jewelry and Bolian crystalsteel. (DS9: "The Jem'Hadar")
The Logicians, an all Vulcan baseball team formed from members of the crew of USS T'Kumbra, featured the Vulcan IDIC on their ballcaps. (DS9: "Take Me Out to the Holosuite")
Background
The invention of the IDIC by Gene Roddenberry was rumored to have caused friction between him and Leonard Nimoy, who saw it as a cheap ploy to sell replica merchandise to fans.