Uhhh not to be picky or anything but "Tai Chi sword" is somewhat of a misnomer. "Tai Chi" denotes a general style (theres Chen, Yang, Wu, Sun, etc styles of Tai Chi) but not necessarialy the type of sword in question. Lots of other Chinese martial art styles use the type of sword being refered to as well. Its just that Tai Chi, Yang style in particular, got some fame for the use of that type of sword. The basic Chinese double edged straight sword should probably just be called the "Jian" (in mandarin) or "Gim" (in Cantonese).
Tai Chi styles also commonly use various versions of the Chinese Dao (saber or "knife"--literal translation) also, so by calling a sword a "Tai Chi" sword it may not always be clear as to which type of sword one is refering to.