The INCORRECT statement regarding the structure of $$C_{60}$$ is:

$$C_{60}$$ (Buckminsterfullerene) has the structure of a truncated icosahedron, resembling a soccer ball. Let us evaluate each statement:

(1) The six-membered rings are fused to both six and five-membered rings. This is correct. In $$C_{60}$$, each hexagonal ring is surrounded by alternating pentagons and hexagons.

(2) Each carbon atom forms three sigma bonds. This is correct. Every carbon atom in $$C_{60}$$ is $$sp^2$$ hybridised and bonded to three other carbon atoms through sigma bonds.

(3) The five-membered rings are fused only to six-membered rings. This is correct. By the isolated pentagon rule, no two pentagons share an edge in $$C_{60}$$. Each pentagonal ring is completely surrounded by hexagonal rings.

(4) It contains 12 six-membered rings and 24 five-membered rings. This is incorrect. The actual composition of $$C_{60}$$ is 12 pentagonal (five-membered) rings and 20 hexagonal (six-membered) rings. This can be verified using Euler's formula for polyhedra. The statement reverses and incorrectly states the numbers.

The incorrect statement is option (4).