In which type of 3D arrangement have `1^(st)` and IV layer's of sphere are identical

Answer

To solve the question of which type of 3D arrangement has the first and fourth layers of spheres identical, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Layers**:
- We start by defining the layers of spheres in a 3D arrangement. Let's denote the first layer as Layer 1 (A), the second layer as Layer 2 (B), the third layer as Layer 3 (C), and so on.

2. **Identifying the Pattern**:
- The question states that the first layer (A) and the fourth layer are identical. This implies that the arrangement must repeat after a certain number of layers.

3. **Layer Arrangement**:
- If Layer 1 is A, then Layer 2 can be B, Layer 3 can be C, and for Layer 4 to be identical to Layer 1, it must also be A. Thus, we have:
- Layer 1: A
- Layer 2: B
- Layer 3: C
- Layer 4: A
- Continuing this pattern, Layer 5 will be B, Layer 6 will be C, and so forth.

4. **Recognizing the Sequence**:
- The sequence of layers can be summarized as:
- Layer 1: A
- Layer 2: B
- Layer 3: C
- Layer 4: A
- Layer 5: B
- Layer 6: C
- This shows a repeating pattern of ABC.

5. **Identifying the Arrangement Type**:
- The arrangement ABC ABC indicates a specific type of packing in three dimensions. This is characteristic of the Cubic Close Packing (CCP) structure, also known as Face-Centered Cubic (FCC) packing.

6. **Conclusion**:
- Therefore, the type of 3D arrangement in which the first and fourth layers of spheres are identical is the **Cubic Close Packing (CCP)** arrangement.

### Final Answer:
The answer is **Cubic Close Packing (CCP)**.