Riker's cap with a placard representing the 102nd
The 102nd New York Infantry was a military unit based out of New York state that made up a portion of the Union Army during the American Civil War. In 1864 the 102nd was under the direct command of Colonel Thaddius Riker.
That summer, the 102nd participated in Sherman's March on Atlanta, including the Battle of Pine Mountain. (VOY: "Death Wish")
Riker's cap, or at least a reproduction of it, was kept in the ready room of William Riker aboard the USS Titan in 2381 along with a placard indicating the 102nd. (LD: "Kayshon, His Eyes Open")
The 102nd New York Regiment did fight in the Atlanta Campaign under Sherman in 1864. It served in the 3rd Brigade of the 2nd Division, XX Corps under Joseph Hooker. Previously, it had formed part of the XII Corps and fought at such engagements as Antietam, Chancellorsville, and Gettysburg. However, no Colonel Thaddius Riker ever commanded the regiment. The colonels in command during the Atlanta Campaign were Col. James C. Lane and Col. Herbert von Hammerstein.