Platonic hydrocarbons are the molecular

Molecule

A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

 representation of platonic solid

Platonic solid

In geometry, a Platonic solid is a convex polyhedron that is regular, in the sense of a regular polygon. Specifically, the faces of a Platonic solid are congruent regular polygons, with the same number of faces meeting at each vertex; thus, all its edges are congruent, as are its vertices and...

 geometries with vertices replaced by carbon

Carbon

Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...

 atom

Atom

The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

s and with edges replaced by chemical bond

Chemical bond

A chemical bond is an attraction between atoms that allows the formation of chemical substances that contain two or more atoms. The bond is caused by the electromagnetic force attraction between opposite charges, either between electrons and nuclei, or as the result of a dipole attraction...

s. Not all platonic solids have an organic molecular counterpart:

• Tetravalent carbon excludes an icosahedron
  Icosahedron
  In geometry, an icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids....
  
   since 5 edges meet at each vertex; the possibility of pentacoordinate carbon, such as CH₅⁺, being available is remote, although this icosahedrane structure, along with octahedrane, has been observed in boron
  Boron
  Boron is the chemical element with atomic number 5 and the chemical symbol B. Boron is a metalloid. Because boron is not produced by stellar nucleosynthesis, it is a low-abundance element in both the solar system and the Earth's crust. However, boron is concentrated on Earth by the...
  
   compounds.
• Angle strain
  Angle strain
  Angle strain, also called Baeyer strain in cyclic molecules, is the resistance associated with bond angle compression or bond angle expansion. It occurs when bond angles deviate from the ideal bond angles to achieve maximum bond strength in a specific chemical conformation...
  
   prevents formation of an octahedron
  Octahedron
  In geometry, an octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex....
  
  , and since 4 edges meet at each corner, there would be no hydrogen atoms, thus this hypothetical octahedron molecule would be an allotrope C₆ of elemental carbon, not a hydrocarbon. The possible existence of this cannot simply be dismissed, although it is unlikely.

The following platonic hydrocarbons, on the other hand, have been synthesised

Chemical synthesis

In chemistry, chemical synthesis is purposeful execution of chemical reactions to get a product, or several products. This happens by physical and chemical manipulations usually involving one or more reactions...

:

• Cubane
  Cubane
  Cubane is a synthetic hydrocarbon molecule 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. It was first synthesized in 1964 by Philip Eaton, a...
  
   (C₈H₈);
• Dodecahedrane
  Dodecahedrane
  Dodecahedrane is a chemical compound first synthesised by Leo Paquette of Ohio State University in 1982, primarily for the "aesthetically pleasing symmetry of the dodecahedral framework"....
  
   (C₂₀H₂₀).

Tetrahedrane

Tetrahedrane

Tetrahedrane is a platonic hydrocarbon with chemical formula 44 and a tetrahedral structure. Extreme angle strain prevents this molecule from forming naturally....

 (C₄H₄) has not yet been synthesized, but it is predicted to be kinetically stable in spite of the acute bond angle and consequent angle strain. Tetrahedral hydrocarbons, including tetrahedrane with tert-butyl substituents and with trimethylsilyl

Trimethylsilyl

A trimethylsilyl group is a functional group in organic chemistry. This group consists of three methyl groups bonded to a silicon atom [−Si3], which is in turn bonded to the rest of a molecule...

 substituents have been produced.

With increasing number of carbon atoms in the frame, the geometry more closely approximates a sphere, and the space enclosed in the carbon "cage" increases. This trend continues with buckyballs or spherical fullerene

Fullerene

A fullerene is any molecule composed entirely of carbon, in the form of a hollow sphere, ellipsoid, or tube. Spherical fullerenes are also called buckyballs, and they resemble the balls used in association football. Cylindrical ones are called carbon nanotubes or buckytubes...

 (C₆₀). Although not a hydrocarbon, fullerene has the shape of a truncated icosahedron

Truncated icosahedron

In geometry, the truncated icosahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids whose faces are two or more types of regular polygons.It has 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices and 90 edges....

, an Archimedean solid

Archimedean solid

In geometry an Archimedean solid is a highly symmetric, semi-regular convex polyhedron composed of two or more types of regular polygons meeting in identical vertices...

.