When an element exists in 2 or more different forms in the same physical state, these differences are called allotropes and the phenomenon is known as allotropy.
Carbon exists in crystalline and amorphous forms. In crystalline it occurs in three allotropic forms: diamond, graphite and fullerenes.
In a diamond, each carbon atom is linked to 4 other carbon atoms by single bonds only. Each carbon atom is present at the centre of a regular tetrahedron and the other 4 carbon atoms linked to it lie at the corners of regular tetrahedron. Thus diamond exists as a three dimensional network. Since there are no free or mobile electrons, diamond is a bad conductor of electricity. The C-C bond length in diamond is 154 pm. The directional covalent bonds are present through the lattice.