Nanotubes are formed by fullerenes allotrope of carbon.

Answer

**Step-by-Step Text Solution:**

1. **Understanding the Question**: The question states that nanotubes are formed by the fullerene allotrope of carbon. We need to confirm if this statement is correct and explain why.

2. **Definition of Fullerenes**: Fullerenes are a specific allotrope of carbon. They are molecules made entirely of carbon, taking the form of a hollow sphere, ellipsoid, or tube. The most famous fullerene is C60, which has a structure resembling a soccer ball.

3. **Structure of Fullerenes**: Fullerenes have a unique structure where carbon atoms are arranged in a pattern of pentagons and hexagons, similar to the panels on a soccer ball. These carbon atoms are bonded together by strong covalent bonds.

4. **Formation of Carbon Nanotubes**: Carbon nanotubes (CNTs) are cylindrical structures that can be thought of as rolled-up sheets of graphene (a single layer of carbon atoms arranged in a hexagonal lattice). These nanotubes are derived from the fullerene structure, where multiple fullerene units can combine to form a cylindrical shape.

5. **Properties of Carbon Nanotubes**: Carbon nanotubes are known for their exceptional strength and unique electrical and thermal conductivity properties. The strength comes from the numerous covalent bonds present in their structure, which allows them to withstand significant stress.

6. **Conclusion**: Therefore, the statement that "nanotubes are formed by fullerene allotrope of carbon" is correct. Carbon nanotubes are indeed derived from the fullerene structure and possess remarkable properties that make them useful in various applications.

---