An interesting mineral. There is a museum in Franklin, New Jersey which showcases different types of fluorescent calcite crystals which glow different colors under ultraviolet light because they contain manganese. Colorless calcite sometimes shows a cat's eye effect when cut in cabochon form; these are seen as gemstones, but generally it's considered too soft for jewelry.
A certain type of squarish calcite crystal that is transparent will sometimes make you see double when you look through it because it refracts the light passing through them twice (birefringence).