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There are many allotropes of carbon, some are:

  • Amorphous Carbon (No real structure to speak of)
  • Diamond (Tetrahedral Crystalline Structure)
  • Graphite (Hexagonal 'Graphene' Sheets)
  • C-nanotubes (Cylindrical Graphene)
  • Buckyballs (Spherical Graphene)

Note that buckyballs and carbon nanotubes are templates of the 'fullerene family' of carbon allotropes, of which there are many.

Another note: Soot is not an allotrope of carbon, it is a collection of particles left from the incomplete combustion of hydrocarbons. Carbon dioxide (CO2) is not an allotrope since it contains oxygen.

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