Which of the following regular polygons does not tessellate?

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Regular tessellations (or regular tilings) are patterns created by repeating a single type of regular polygon without any gaps or overlaps. In the context of regular polygons, only three types can tessellate the plane by themselves:

1. **Equilateral Triangle**: Each interior angle is 60°, and six triangles meet at each vertex (6 × 60° = 360°).
2. **Square**: Each interior angle is 90°, and four squares meet at each vertex (4 × 90° = 360°).
3. **Regular Hexagon**: Each interior angle is 120°, and three hexagons meet at each vertex (3 × 120° = 360°).

Any regular polygon with a different number of sides does not tessellate the plane on its own. For example:

- **Regular Pentagon**: Each interior angle is 108°. Three pentagons meeting at a vertex would total 324°, which is less than 360°, leaving gaps.
- **Regular Heptagon (7 sides)**: Each interior angle is approximately 128.57°. Two heptagons meet at a vertex for a total of about 257.14°, which again leaves gaps.
  
**Conclusion:**

Among regular polygons, the **regular pentagon** is a common example that does **not** tessellate the plane by itself.

**Answer:** A regular pentagon is a regular polygon that does not tessellate the plane.
A regular pentagon does not tessellate the plane.

Which of the following regular polygons does not tessellate?

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