The most popular form of buckyballs is the C60 which has isosurface which is ground state and its electron density is calculated using DFT. There are various different types of buckyballs. You can learn about all of them at **http://mstnano.com**. A few popular ones are listed below:

- Buckminsterfullerene: This is the smallest molecule of fullerene which has hexagonal and pentagonal rings in which no pentagons would share edges with each other. It is widely found in soot. The structure of C60 is somewhat icosahedrons which looks like a football made up of 20 hexagons and 12 pentagons. A carbon atom is placed at the polygon’s vertices and there is a bond across the edges. The diameter is around 1.1 nanometers. The bond length between two hexagons is 6.6 while between the hexagon and a pentagon is 6.5. on an average, the bond length is 1.4 angstroms.
- Boron buckyball: this buckyball makes use of boron atoms instead of carbon. It was discovered in 2007. Each atom of B80 has 5-6 bonds and is more stable. It has the original geodesic dome structure like Buckminster fuller that has triangles rather than hexagons. It contains 20 six member rings and 12 five member rings. Each six member ring has an extra atom at its center which is bonded to the atom surrounding it. This buckyball is not likely to occur in nature.

- Other buckyballs: Apart from these two other most common fullerene is the C70. There are even fullerenes with 76,72,84 upto 100 atoms of carbon that occur in nature. A common structure of a fullerene is a polyhedron which is trivalent convex in nature. It contains hexagonal and pentagonal faces. In graph theory it is defined that a fullerene is any 3 regular planar graph which has all faces having size either 5 or 6. This includes the external face too. The formula for a fullerene according to Euler’s polyhedron theory is V-E +F =2 where v is vertices, f is faces and e are the edges. In a fullerene there are 12 pentagons found and the number of hexagons equals V/2 -10.
- Dodecahedral: this is the smallest fullerene occurring in nature. It is known as C20. The truncated icosahedrons has no adjacent pair of pentagons. There are heterofullerenes which contain heteroatoms that can substitute the carbons present in cage or in tube shaped structures. These were found in 1993 and has expanded the fullerene class of compounds to a great extent. Some common examples of these are nitrogen aka azafullerene, boron, phosphorous and oxygen derivatives. There are other types too such as Trimetasphere.

These are different types of buckyballs. To know more about fullerenes and their properties visit http://mstnano.com.