For two- dimensional hexagonal lattice, the unit cell is ______

Answer

To determine the unit cell for a two-dimensional hexagonal lattice, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Hexagonal Lattice**:
- A hexagonal lattice is characterized by a repeating pattern that forms a hexagon. In two dimensions, it consists of points arranged in a hexagonal shape.

2. **Drawing the Unit Cell**:
- To visualize the unit cell, we can start by sketching a hexagon. The hexagon will have six vertices, which correspond to the positions of the atoms in the lattice.

3. **Identifying the Atoms in the Unit Cell**:
- In a two-dimensional hexagonal lattice, each corner of the hexagon contains one atom. However, since each corner atom is shared among adjacent unit cells, only a fraction of each atom belongs to the unit cell. Specifically, each corner atom contributes 1/6th to the unit cell.

4. **Calculating the Contribution of Atoms**:
- Since there are six corners in the hexagon, the total contribution from the corner atoms to the unit cell is:
\[ 6 \times \frac{1}{6} = 1 \text{ atom} \]
- Additionally, if there is an atom at the center of the hexagon, it contributes fully (1 atom) to the unit cell.

5. **Finalizing the Unit Cell Description**:
- Therefore, the unit cell for a two-dimensional hexagonal lattice consists of one atom from the corners and potentially one atom at the center, leading to a total of 1 or 2 atoms depending on the specific arrangement.

6. **Conclusion**:
- The unit cell for a two-dimensional hexagonal lattice is a hexagon.

### Final Answer:
The unit cell for a two-dimensional hexagonal lattice is **hexagonal**.