An allotrope is a variant of a substance consisting of only one type of atom. It is a new molecular configuration, with new physical properties. Allotropes of a given substance will often have substantial differences between each other. Generally one allotrope will be far more abundant than another.
Oxygen has three known allotropes, O2 which is far more abundant than O3, ozone and O4, tetraoxygen.
Phosphorous comes in at least 3 allotropic forms; red, black (or purple, or violet), white (or yellow). Red and white phosphorous are the most common, both of which consist of tetrahedrally arranged groups of four phosphorous. The tetrahedral arrangements in red phosphorous are linked into chains, whereas those in white phosphorous are separate. Black phosphorous is arranged in 2-dimensional hexagonal sheets, much like graphite. White prosphorous reacts immediately to the air, oxiding and producing phosphorus pentoxide.
Carbon is the substance with the greatest number of allotropes, with 8 discovered so far. It possesses allotropes most radically different from one another, ranging from soft to hard, opaque to transparent, abrasive to smooth, inexpensive to costly. These allotropes include the amorphous carbonallotrope, carbon nanofoam, carbon nanotube, the diamond allotrope, fullerene allotrope, graphite, lonsdaleite, and ceraphite allotrope. Coal and soot are both forms of amorphous carbon, one of the most common carbon allotropes. Diamond is an allotrope in which atoms are linked in a 3-D crystalline network of covalent carbon bonds. Diamond, of course, is both very expensive, rare, and strong. Carbon fullerenes are among the strongest and lightest materials known. Carbon nanofoam has an extremely low density, only a few times heavier than air.

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