If all three interfacial angels defining the unit cell, are equal in magnitude, the crystal cannot be:

Options

A. rhombohedral
B. cubic
C. hexagonal
D. tetragonal

Answer

To solve the question, "If all three interfacial angles defining the unit cell are equal in magnitude, the crystal cannot be:", we need to analyze the characteristics of different crystal systems based on their interfacial angles.

### Step-by-Step Solution:

1. **Understanding Interfacial Angles**:
- The interfacial angles in a crystal system are denoted as alpha (α), beta (β), and gamma (γ).
- The question states that all three angles are equal in magnitude, i.e., α = β = γ.

2. **Identifying Crystal Systems**:
- There are seven crystal systems: cubic, tetragonal, orthorhombic, rhombohedral, hexagonal, monoclinic, and triclinic.
- We will analyze each system to see if it can have all three angles equal.

3. **Cubic System**:
- In the cubic system, α = β = γ = 90°.
- Since all angles are equal, this system can exist under the given condition.

4. **Tetragonal System**:
- In the tetragonal system, α = β = γ = 90°.
- Similar to the cubic system, this system can also exist with equal angles.

5. **Rhombohedral System**:
- In the rhombohedral system, α, β, and γ are equal but not equal to 90° (they are typically less than 90°).
- Therefore, this system cannot have all three angles equal to each other in the sense of being equal to 90°.

6. **Hexagonal System**:
- In the hexagonal system, two angles (α and β) are equal (90°), while γ = 120°.
- Hence, this system also cannot have all three angles equal.

7. **Conclusion**:
- The crystal systems that cannot have all three interfacial angles equal in magnitude are the **rhombohedral** and **hexagonal** systems.

### Final Answer:
The crystal cannot be **rhombohedral** and **hexagonal**.