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What is an allotrope?

What is an allotrope? Here are some definitions.

Noun
  1. (chemistry) Any form of an element that has a distinctly different molecular structure to another form of the same element. [from 1847]
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The second allotrope, gray or alpha tin, has a face-centred cubic structure.
Neither allotrope dissolves in water, but both dissolve in organic liquids, such as benzene, carbon tetrachloride, and carbon disulfide.
Carbon nanofoams are the fifth known allotrope of carbon, after graphite, diamond, carbon nanofibers and fullerenes.
An orthorhombic modification, S12 ring molecules, and still another unstable S10 ring allotrope are reported.
A third allotrope occurs as an amorphous brown powder with a density of 2.350 grams per cubic centimeter.
Incredibly lightweight carbon nanofoams, essentially a fifth major allotrope of carbon, were discovered several years ago.

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