Allotropes:
diamond
graphite
fullerene
graphene;
Structures:
Diamond:
tetrahedral arrangement of (carbon) atoms/each carbon bonded to four others / sp3 and 3D/covalent network structure;
Graphite:
each carbon bonded to three others (in a trigonal planar arrangement) / sp2 and 2D / layers of (carbon) atoms;
Fullerene:
each (carbon) atom bonded to three others (in a trigonal arrangement) / sp2 and joined in a ball/cage/sphere/connected hexagons and pentagons;
Graphene:
each carbon bonded to three others (in a trigonal arrangement) / sp2 and 2D structure;