Carbon planets are a theoretical type of terrestrial planet that form in carbon rich (and oxygen poor) protoplanetary disks. The core would be iron rich and surrounded by silicon carbide and titanium carbide. The mantle would be mainly made of graphite and multi-kilometer thick layer of diamond (if there is sufficient pressure. The surface would be abundant in hydrocarbons and carbon monoxide.
Carbon planets are predicted to be of similar diameter to silicate and water planets of the same mass, potentially making them difficult to distinguish.
For carbon planets to form, it would be necessary for the protoplanetary disc of the host star to be carbon-rich, and oxygen-poor. Such stars exist near the center of galaxy.  As stars age, they tend to produce more carbon, and as the interstellar medium is enriched with heavier elements through the deaths of old stars, carbon planets may become more common as the universe ages.