Hydrocarbons that have the same molecular geometry as the five Platonic solids, i.e. the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosahedron. These hydrocarbons have carbon atoms at the vertices of the polyhedra and single bonds along the edges. In fact, there are only two known Platonic hydrocarbons: cubane (C₈H₈) and dodecahedrane (C₂₀H₂₀). The hydrocarbon based on a tetrahedron (C₄H₄) does not exist because of angle strain, but substituted derivatives C₄X₄ are known. Angle strain is also the reason for the nonexistence of octahedrane (C₆H₆) and icosahedrane (C₁₂H₁₂). A major difficulty that has prevented the synthesis of icosahedrane (C₁₂H₁₂) is that it is very difficult to reconcile the necessity of five edges meeting at a vertex with carbon being quadrivalent.