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Image:Tetrahedrane-3D-balls.png ,
In organic chemistry
Organic chemistry is a subdiscipline within chemistry involving the scientific study of the structure, properties, and reactions of organic compounds and organic materials, i.e., matter in its various forms that contain carbon atoms.Clayden, J.; ...
, a Platonic hydrocarbon is a hydrocarbon
In organic chemistry, a hydrocarbon is an organic compound consisting entirely of hydrogen and carbon. Hydrocarbons are examples of group 14 hydrides. Hydrocarbons are generally colourless and hydrophobic, and their odors are usually weak or ex ...
(molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
) whose structure
A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such as ...
matches one of the five 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 c ...
s, with carbon
Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent
In chemistry, the valence (US spelling) or valency (British spelling) of an element is the measure of its combining capacity with o ...
atoms replacing its vertices, carbon–carbon bond
A carbon–carbon bond is a covalent bond between two carbon atoms. The most common form is the single bond: a bond composed of two electrons, one from each of the two atoms. The carbon–carbon single bond is a sigma bond and is formed b ...
s replacing its edges, and hydrogen atoms as needed.
Not all Platonic solids have molecular hydrocarbon counterparts; those that do are the tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the o ...
(tetrahedrane
Tetrahedrane is a hypothetical platonic hydrocarbon with chemical formula and a tetrahedral structure. The molecule would be subject to considerable angle strain and has not been synthesized as of 2021. However, a number of derivatives have bee ...
), the cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross.
The cube is the only r ...
(cubane
Cubane () is a synthetic hydrocarbon compound that consists of eight carbon atoms arranged at the corners of a cube, with one hydrogen atom attached to each carbon atom. A solid crystalline substance, cubane is one of the Platonic hydrocarbons an ...
), and the dodecahedron
In geometry, a dodecahedron (Greek , from ''dōdeka'' "twelve" + ''hédra'' "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagon ...
(dodecahedrane
Dodecahedrane is a chemical compound, a hydrocarbon with formula , whose carbon atoms are arranged as the vertices (corners) of a regular dodecahedron. Each carbon is bound to three neighbouring carbon atoms and to a hydrogen atom. This compound ...
).
Tetrahedrane
Tetrahedrane
Tetrahedrane is a hypothetical platonic hydrocarbon with chemical formula and a tetrahedral structure. The molecule would be subject to considerable angle strain and has not been synthesized as of 2021. However, a number of derivatives have bee ...
(C4H4) is a hypothetical compound
A hypothetical chemical compound is a chemical compound that has been conceived of, but is not known to have been synthesized, observed, or isolated (identified or shown to exist).
Some hypothetical compounds cannot form at all. Others might tur ...
. It has not yet been synthesized without substituent
A substituent is one or a group of atoms that replaces (one or more) atoms, thereby becoming a moiety in the resultant (new) molecule. (In organic chemistry and biochemistry, the terms ''substituent'' and ''functional group'', as well as ''side ...
s, but it is predicted to be kinetically stable
A stable is a building in which livestock, especially horses, are kept. It most commonly means a building that is divided into separate stalls for individual animals and livestock. There are many different types of stables in use today; the ...
in spite of its angle strain. Some stable derivative
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. F ...
s, including tetra( ''tert''-butyl)tetrahedrane (a hydrocarbon) and tetra(trimethylsilyl
A trimethylsilyl group (abbreviated TMS) is a functional group in organic chemistry. This group consists of three methyl groups bonded to a silicon atom minus;Si(CH3)3 which is in turn bonded to the rest of a molecule. This structural group is ch ...
)tetrahedrane, have been produced.
Cubane
Cubane
Cubane () is a synthetic hydrocarbon compound that consists of eight carbon atoms arranged at the corners of a cube, with one hydrogen atom attached to each carbon atom. A solid crystalline substance, cubane is one of the Platonic hydrocarbons an ...
(C8H8) has been synthesized. Although it has high angle strain, cubane is kinetically stable, due to a lack of readily available decomposition paths.
Octahedrane
Angle strain
In organic chemistry, ring strain is a type of instability that exists when bonds in a molecule form angles that are abnormal. Strain is most commonly discussed for small rings such as cyclopropanes and cyclobutanes, whose internal angles are su ...
would make an octahedron
In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at ea ...
highly unstable due to inverted tetrahedral 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 ...
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
Allotropy or allotropism () is the property of some chemical elements to exist in two or more different forms, in the same physical state, known as allotropes of the elements. Allotropes are different structural modifications of an element: the ...
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
Dodecahedrane is a chemical compound, a hydrocarbon with formula , whose carbon atoms are arranged as the vertices (corners) of a regular dodecahedron. Each carbon is bound to three neighbouring carbon atoms and to a hydrogen atom. This compound ...
(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.
Icosahedrane
The tetravalency (4-connectedness) of carbon excludes anicosahedron
In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons".
There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrica ...
because 5 edges meet at each vertex. True pentavalent carbon is unlikely; methanium
In chemistry, methanium is a complex positive ion with formula []+, namely a molecule with one carbon atom covalent bond, bonded to three hydrogen atoms and one hydrogen molecule, bearing a +1 electric charge. It is a superacid and one of the ...
, nominally , usually exists as . The hypothetical icosahedral lacks hydrogen so it is not a hydrocarbon; it is also an ion.
Both icosahedral and octahedral structures have been observed in boron
Boron is a chemical element with the symbol B and atomic number 5. In its crystalline form it is a brittle, dark, lustrous metalloid; in its amorphous form it is a brown powder. As the lightest element of the ''boron group'' it has th ...
compounds such as the dodecaborate
The dodecaborate(12) anion, 12H12sup>2−, is a borane with an icosahedral arrangement of 12 boron atoms, with each boron atom being attached to a hydrogen atom. Its symmetry is classified by the molecular point group Ih.
Synthesis and reaction ...
ion and some of the carbon-containing carborane
Carboranes are electron-delocalized (non-classically bonded) clusters composed of boron, carbon and hydrogen atoms.Grimes, R. N., ''Carboranes 3rd Ed.'', Elsevier, Amsterdam and New York (2016), . Like many of the related boron hydrides, these cl ...
s.
Other polyhedra
Increasing the number of atoms that comprise thecarbon skeleton
The skeletal formula, or line-angle formula or shorthand formula, of an organic compound is a type of molecular structural formula that serves as a shorthand representation of a molecule's bonding and some details of its molecular geometry. A ...
leads to a geometry that increasingly approximates a sphere, and the space enclosed in the carbon "cage" increases. This trend continues with buckyballs or spherical fullerene
A fullerene is an allotrope of carbon whose molecule consists of carbon atoms connected by single and double bonds so as to form a closed or partially closed mesh, with fused rings of five to seven atoms. The molecule may be a hollow sphere, ...
(C60). Although not a Platonic hydrocarbon, buckminsterfullerene has the shape of a truncated icosahedron
In geometry, the truncated icosahedron is an Archimedean solid, one of 13 convex isogonal nonprismatic solids whose 32 faces are two or more types of regular polygons. It is the only one of these shapes that does not contain triangles or squares. ...
, an Archimedean solid
In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes. They are the convex uniform polyhedra composed of regular polygons meeting in identical vertices, excluding the five Platonic solids (which are composed ...
.
The concept can also be extended to regular Euclidean tilings, with the hexagonal tiling
In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex. It has Schläfli symbol of or (as a truncated triangular tiling).
English mathemat ...
producing graphane
Graphane is a two-dimensional polymer of carbon and hydrogen with the formula unit (CH)n where ''n'' is large. Partial hydrogenation results in hydrogenated graphene, which was reported by Elias et al in 2009 by a TEM study to be "direct evidence ...
. A square tiling
In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane. It has Schläfli symbol of meaning it has 4 squares around every vertex.
Conway called it a quadrille.
The internal angle of the s ...
(which would resemble an infinitely large fenestrane
A fenestrane in organic chemistry is a type of chemical compound with a central quaternary carbon atom which serves as a common vertex for four fused carbocycles. They can be regarded as spiro compounds twice over. Because of their inherent strai ...
) would suffer from the same problem as octahedrane, and the triangular tiling
In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane, and is the only such tiling where the constituent shapes are not parallelogons. Because the internal angle of the equilater ...
icosahedrane. No generalisations to hyperbolic tilings seem to be known.
The regular convex 4-polytope
In mathematics, a regular 4-polytope is a regular four-dimensional polytope. They are the four-dimensional analogues of the regular polyhedra in three dimensions and the regular polygons in two dimensions.
There are six convex and ten star regu ...
s may also have hydrocarbon analogues; hypercubane has been proposed.
Gallery
Tetrahedrane
Tetrahedrane is a hypothetical platonic hydrocarbon with chemical formula and a tetrahedral structure. The molecule would be subject to considerable angle strain and has not been synthesized as of 2021. However, a number of derivatives have bee ...
Image:Cubane-3D-balls.png , Cubane
Cubane () is a synthetic hydrocarbon compound that consists of eight carbon atoms arranged at the corners of a cube, with one hydrogen atom attached to each carbon atom. A solid crystalline substance, cubane is one of the Platonic hydrocarbons an ...
Image:Dodecahedrane-3D-balls.png, Dodecahedrane
Dodecahedrane is a chemical compound, a hydrocarbon with formula , whose carbon atoms are arranged as the vertices (corners) of a regular dodecahedron. Each carbon is bound to three neighbouring carbon atoms and to a hydrogen atom. This compound ...
References
{{Commons category, Platonic hydrocarbons Hydrocarbons Hypothetical chemical compoundsHydrocarbons
In organic chemistry, a hydrocarbon is an organic compound consisting entirely of hydrogen and carbon. Hydrocarbons are examples of group 14 hydrides. Hydrocarbons are generally colourless and hydrophobic, and their odors are usually weak or ex ...