Carnelian is a clear-to-translucent reddish-brown variety of chalcedony colored by impurities of iron oxide. You can get mixed colours from clear through yellow, orange and up to a deep red.
The earliest carvings I could find reference to are beads which were carved in the Early Neolithic in Bulgaria. Needless to say it has been carved for a long time!
It is found around the world but most of ours in New Zealand seems to come from the Coromandel.
Because it is so translucent it really suits reverse intaglio – where you carve into the back of the stone like the little Ruru below or intaglio (carved into the front like the Huia below).