Tessellation Explorer
About This MicroSim
This interactive visualization demonstrates the three regular tessellations - patterns that tile the plane using only one type of regular polygon with no gaps or overlaps.
Why Only Three?
For a regular polygon to tessellate by itself, the interior angles meeting at each vertex must sum to exactly 360°.
| Polygon | Interior Angle | Calculation | Tessellates? |
|---|---|---|---|
| Triangle | 60° | 6 × 60° = 360° | Yes |
| Square | 90° | 4 × 90° = 360° | Yes |
| Pentagon | 108° | 3 × 108° = 324° (gap) | No |
| Hexagon | 120° | 3 × 120° = 360° | Yes |
| Heptagon | ~128.6° | Cannot reach 360° exactly | No |
Key Observation
- Triangles: 6 triangles meet at each vertex
- Squares: 4 squares meet at each vertex
- Hexagons: 3 hexagons meet at each vertex
The red circle highlights a vertex where you can see exactly how the shapes fit together.
Interactions
- Click buttons to switch between the three tessellation types
- Observe the vertex angle sum calculation in the info panel
Learning Objectives
- Understand why only three regular polygons tessellate alone
- Apply the interior angle formula to verify tessellation conditions
- Recognize the 360° requirement at each vertex
Bloom's Taxonomy Level
Applying and Evaluating