Describe and compare three features of the structure and bonding in the three allotropes of carbon: diamond, graphite and C60 fullerene.

Diamond, graphite, and C60 fullerene are all different allotropes of carbon, which means they have the same chemical composition but different arrangements of atoms and different physical properties.

1. Structure: Diamond is a three-dimensional covalent network structure in which each carbon atom is bonded to four other carbon atoms in a tetrahedral arrangement, resulting in a very hard and rigid material with a high melting point. Graphite, on the other hand, is made up of layers of hexagonally arranged carbon atoms that are bonded covalently within each layer but held together by weak van der Waals forces between layers, resulting in a soft and slippery material. C60 fullerene has a hollow, cage-like structure made up of 60 carbon atoms arranged in a series of hexagons and pentagons, resembling a soccer ball.
2. Bonding: In diamond, each carbon atom forms four strong covalent bonds with its neighboring carbon atoms, resulting in a very strong and stable material. In graphite, each carbon atom forms three covalent bonds with neighboring carbon atoms within a layer, and the fourth electron is delocalized and forms weak van der Waals forces between layers, resulting in a softer and more flexible material. C60 fullerene, like diamond, is held together by strong covalent bonds between the carbon atoms in the hexagons and pentagons that make up its cage-like structure.
3. Properties: Diamond is a very hard and transparent material with a high refractive index, making it useful in jewelry and as an abrasive. Graphite is a soft and slippery material that is used in pencils and as a lubricant. C60 fullerene has unique electronic and optical properties, and its hollow structure makes it useful in areas such as drug delivery and nanotechnology.

In summary, the different allotropes of carbon have different structures and bonding arrangements that result in different physical and chemical properties. Diamond has a three-dimensional covalent network structure, graphite has layered hexagonal arrangements with weak van der Waals forces between layers, and C60 fullerene has a cage-like structure held together by strong covalent bonds. Each allotrope has unique properties and applications based on its structure and bonding.