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Concept# Platonic hydrocarbon

Summary

In organic chemistry, a Platonic hydrocarbon is a hydrocarbon (molecule) whose structure matches one of the five Platonic solids, with carbon atoms replacing its vertices, carbon–carbon bonds replacing its edges, and hydrogen atoms as needed.
Not all Platonic solids have molecular hydrocarbon counterparts; those that do are the tetrahedron (tetrahedrane), the cube (cubane), and the dodecahedron (dodecahedrane).
Tetrahedrane
Tetrahedrane (C4H4) is a hypothetical compound. It has not yet been synthesized without substituents, but it is predicted to be kinetically stable in spite of its angle strain. Some stable derivatives, including tetra(tert-butyl)tetrahedrane (a hydrocarbon) and tetra(trimethylsilyl)tetrahedrane, have been produced.
Cubane
Cubane (C8H8) has been synthesized. Although it has high angle strain, cubane is kinetically stable, due to a lack of readily available decomposition paths.
Angle strain would make an octahedron highly unstable due to inverted tetrahedral geometry at each vertex. There would also be no hydrogen atoms because four edges meet at each corner; thus, the hypothetical octahedrane molecule would be an allotrope of elemental carbon, C6, and not a hydrocarbon. The existence of octahedrane cannot be ruled out completely, although calculations have shown that it is unlikely.
Dodecahedrane
Dodecahedrane (C20H20) was first synthesized in 1982, and has minimal angle strain; the tetrahedral angle is 109.5° and the dodecahedral angle is 108°, only a slight discrepancy.
The tetravalency (4-connectedness) of carbon excludes an icosahedron because 5 edges meet at each vertex. True pentavalent carbon is unlikely; methanium, nominally CH5+, usually exists as CH3(H2)+. The hypothetical icosahedral C1212+ lacks hydrogen so it is not a hydrocarbon; it is also an ion.
Both icosahedral and octahedral structures have been observed in boron compounds such as the dodecaborate ion and some of the carbon-containing carboranes.

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Tetrahedral molecular geometry

In a tetrahedral molecular geometry, a central atom is located at the center with four substituents that are located at the corners of a tetrahedron. The bond angles are cos−1(−) = 109.4712206...° ≈ 109.5° when all four substituents are the same, as in methane () as well as its heavier analogues. Methane and other perfectly symmetrical tetrahedral molecules belong to point group Td, but most tetrahedral molecules have lower symmetry. Tetrahedral molecules can be chiral.

Platonic solid

In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex. There are only five such polyhedra: Geometers have studied the Platonic solids for thousands of years. They are named for the ancient Greek philosopher Plato who hypothesized in one of his dialogues, the Timaeus, that the classical elements were made of these regular solids.

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