Due to high refractive index its critical angle is very small so that most of the light incident on the diamond is total internally reflected repeatedly and diamond sparkles.

* A fullerene is an allotrope of carbon which form a closed mesh with fused rings of five to seven carbon atoms connected with single and double bonds.

* The molecular formula of  fullerene is  C₆₀ and informally it is called buckyballs.

* The structure of C₆₀ is a truncated icosahedron, which resembles an association football ball.

Allotropes are different forms of the same element. Different bonding arrangements between atoms result in different structures with different chemical and physical properties.

* Fullerene, also called buckminsterfullerene, is an allotrope of carbon. It is a cage-like structure in which molecules are composed of 60 carbon atoms (C60) joined together by single and double bonds to form a hollow sphere with 12 pentagonal and 20 hexagonal faces—a design that resembles a football, or soccer ball.

* Graphene is a one-atom-thick layer of carbon atoms arranged in a hexagonal lattice. It is the crystalline allotrope of carbon. It is the building-block of Graphite (which is used, among others things, in pencil tips). Hence, statement 1 is correct

Graphene is a good conductor of electricity because one carbon atom is bonded only with three carbon atoms, which enables the presence of free electrons. Fullerenes in pure state act as insulators but can be converted to semiconductors and superconductors under suitable conditions. Hence, statement 2 is incorrect.

* Statement 1 is correct: Both diamond and graphite are formed by carbon atoms, the difference lies in the manner in which the carbon atoms are bonded to one another.

* In diamond, each carbon atom is bonded to four other carbon atoms forming a rigid three-dimensional structure.

* In graphite, each carbon atom is bonded to three other carbon atoms in the same plane giving a hexagonal array. One of these bonds is a double-bond, and thus the valency of carbon is satisfied.

* Statement 2 is incorrect: Graphite structure is formed by the hexagonal arrays being placed in layers one above the other.

* These two different structures result in diamond and graphite having very different physical properties even though their chemical properties are the same.

* Diamond is the hardest substance known while graphite is smooth and slippery. Graphite is also a very good conductor of electricity unlike other non-metals.

* Diamonds can be synthesised by subjecting pure carbon to very high pressure and temperature. These synthetic diamonds are small but are otherwise indistinguishable from natural diamonds.

* Statement 3 is incorrect: Fullerenes form another class of carbon allotropes not an isotope.

* The first one to be identified was C-60 which has carbon atoms arranged in the shape of a football not all fullerene.

* Since this looked like the geodesic dome designed by the US architect Buckminster Fuller, the molecule was named fullerene.