Which of the following given crystal system is the most symmetrical and the most unsymmetrical system respectively?

Options

A. Cubic, Hexagonal
B. Orthorhombic, Monoclinic
C. Cubic, Tridinic
D. Rhombohedral, Tetragonal

Answer

To determine which crystal systems are the most symmetrical and the most unsymmetrical, we need to analyze the properties of different crystal systems based on their axial lengths and interaxial angles.

### Step-by-Step Solution:

1. **Understanding Crystal Systems**:
- Crystal systems are categorized based on their symmetry properties, which are defined by the lengths of their axes (a, b, c) and the angles between them (α, β, γ).
- The most symmetrical crystal system will have all axes equal in length and all angles equal.

2. **Identifying the Most Symmetrical System**:
- The most symmetrical crystal system is the **Cubic System**. In this system:
- \( a = b = c \)
- \( \alpha = \beta = \gamma = 90^\circ \)
- This means all sides are equal, and all angles are right angles.

3. **Identifying the Most Unsymmetrical System**:
- The most unsymmetrical crystal system is the **Triclinic System**. In this system:
- \( a \neq b \neq c \)
- \( \alpha \neq \beta \neq \gamma \)
- This indicates that all sides are of different lengths and all angles are different.

4. **Matching with Options**:
- The options provided are:
- A) Cubic and Hexagonal
- B) Orthorhombic and Monoclinic
- C) Cubic and Triclinic
- D) Rhombohedral and Tetragonal
- From our analysis, the correct answer is **C) Cubic and Triclinic**.

### Final Answer:
The most symmetrical crystal system is **Cubic**, and the most unsymmetrical system is **Triclinic**.

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