Platonic hydrocarbons vs platonic solids

organic chemistry Organic chemistry is a subdiscipline within chemistry involving the science, scientific study of the structure, properties, and reactions of organic compounds and organic matter, organic materials, i.e., matter in its various forms that contain ...

, 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 Hydrophobe, hydrophobic; their odor is usually fain ...

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 polytope, convex, regular polyhedron in three-dimensional space, three-dimensional Euclidean space. Being a regular polyhedron means that the face (geometry), faces are congruence (geometry), congruent (id ...

s, with

carbon Carbon () is a chemical element; it has chemical symbol, symbol C and atomic number 6. It is nonmetallic and tetravalence, tetravalent—meaning that its atoms are able to form up to four covalent bonds due to its valence shell exhibiting 4 ...

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 between on ...

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 (: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular Face (geometry), faces, six straight Edge (geometry), edges, and four vertex (geometry), vertices. The tet ...

(

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 . However, a number of derivatives have been prepa ...

), the

cube A cube or regular hexahedron is a three-dimensional space, three-dimensional solid object in geometry, which is bounded by six congruent square (geometry), square faces, a type of polyhedron. It has twelve congruent edges and eight vertices. It i ...

(

cubane Cubane is a synthetic hydrocarbon compound with the Chemical formula, formula . It consists of eight carbon atoms arranged at the corners of a Cube (geometry), cube, with one hydrogen atom attached to each carbon atom. A solid crystalline substanc ...

), and the

dodecahedron In geometry, a dodecahedron (; ) or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. There are also three Kepler–Po ...

(

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 ...

). The possibility and existence of each platonic hydrocarbon is affected by the number of bonds to each carbon vertex and the

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 ...

between the bonds at each vertex.

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 . However, a number of derivatives have been prepa ...

(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, due to steric ef ...

. It has not yet been synthesized without

substituent In organic chemistry, a substituent is one or a group of atoms that replaces (one or more) atoms, thereby becoming a moiety in the resultant (new) molecule. The suffix ''-yl'' is used when naming organic compounds that contain a single bond r ...

s, but it is predicted to be kinetically

stable A stable is a building in which working animals are kept, especially horses or oxen. The building is usually divided into stalls, and may include storage for equipment and feed. Styles There are many different types of stables in use tod ...

in spite of its angle strain. Some stable

derivative In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is t ...

s, including tetra( ''tert''-butyl)tetrahedrane 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 i ...

)tetrahedrane, have been produced.

Cubane

Cubane Cubane is a synthetic hydrocarbon compound with the Chemical formula, formula . It consists of eight carbon atoms arranged at the corners of a Cube (geometry), cube, with one hydrogen atom attached to each carbon atom. A solid crystalline substanc ...

(C₈H₈) has been synthesized. Although it has high angle strain, cubane is

kinetically stable In chemistry and physics, metastability is an intermediate energetic state within a dynamical system other than the system's state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. If the ball is onl ...

, due to a lack of readily available decomposition paths.

Octahedrane

Angle strain would make an

octahedron In geometry, an octahedron (: octahedra or octahedrons) is any polyhedron with eight faces. One special case is the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex. Many types of i ...

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 arccos(−) = 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, with a

molecular formula A chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, such as paren ...

of C₆, 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 rather than 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 an

icosahedron In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes . The plural can be either "icosahedra" () or "icosahedrons". There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrical tha ...

because 5 edges meet at each vertex. True pentavalent carbon is unlikely;

methanium In chemistry, methanium is a complex positive ion with formula (metastable transitional form, a carbon atom covalently bonded to five hydrogen atoms) or (fluxional form, namely a molecule with one carbon atom covalently bonded to three hydro ...

, 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; it has 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 three ...

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 re ...

ion and some of the carbon-containing

carborane Carboranes (or carbaboranes) 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 ...

Other polyhedra

Increasing the number of atoms that comprise the carbon skeleton 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 allotropes of carbon, allotrope of carbon whose molecules consist 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 six atoms. The molecules may ...

(C₆₀). Although not a Platonic hydrocarbon,

buckminsterfullerene Buckminsterfullerene is a type of fullerene with the formula . It has a cage-like fused-ring structure ( truncated icosahedron) made of twenty hexagons and twelve pentagons, and resembles a football. Each of its 60 carbon atoms is bonded to i ...

has the shape of a

truncated icosahedron In geometry, the truncated icosahedron is a polyhedron that can be constructed by Truncation (geometry), truncating all of the regular icosahedron's vertices. Intuitively, it may be regarded as Ball (association football), footballs (or soccer ...

, an

Archimedean solid The Archimedean solids are a set of thirteen convex polyhedra whose faces are regular polygon and are vertex-transitive, although they aren't face-transitive. The solids were named after Archimedes, although he did not claim credit for them. They ...

. 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 Truncation (geometry), truncated triangular tiling ...

producing graphane. A

square tiling In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane consisting of four squares around every vertex. John Horton Conway called it a quadrille. Structure and properties The square tili ...

(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 st ...

) 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 or regular polychoron 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 co ...

s may also have hydrocarbon analogues;

hypercubane Hypercubane is a hypothetical polycyclic hydrocarbon with the chemical formula C40H24. It is a molecular analog of the four-dimensional hypercube or tesseract. Hypercubane possesses an unconventional geometry of the carbon framework. It has ''Oh'' ...

has been proposed.

References

{{Commons category, Platonic hydrocarbons Hydrocarbons Hypothetical chemical compounds

Hydrocarbons 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; their odor is usually faint, and may b ...