I think this speaks for itself. ;O
Carbink could be based on the carbuncle, a mythical fairy-like creature that was rumored to have gemstones growing out of it.
Also, when searching Carbuncle, search "carbuncle gemstone". Carbuncle more frequently refer to boils (ew ew ew).
Note that Carbink also has Diamonds sticking out of it, so it's more likely a mixture of gems.
Also, any gem can look like how Carbink's main body looks; uncut gems come in all shapes and forms.