What are diamond and graphite in relation to carbon?

They're both carbon allotropes, however they are arranged differently. Diamond and graphite are both allotropes of carbon. Allotropes are basically different forms of the same element. The only difference is the structure and arrangement of how the carbon atoms are oriented. As you can see, graphite is arranged in a sheet-like arrangement and when used in pencils, sheets of graphite are removed when writing. As for diamonds, they are arranged in a geometric, 3D shape. This is the reason why they are considered the hardest, natural compound. Hope this helps :)

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