Real-World Examples of Tessellations in Architecture and Nature

📚 Quick Study Guide

• 🧩 Definition: A tessellation (or tiling) is a pattern of shapes that fit together without any gaps or overlaps.
• 📐 Regular Tessellations: Made up of only one type of regular polygon (e.g., equilateral triangles, squares, or hexagons).
• 🔶 Semi-Regular Tessellations: Made up of two or more different regular polygons.
• 🌳 Nature's Examples: Honeycomb (hexagons), reptile scales, some crystal structures.
• 🏛️ Architectural Examples: Islamic art (geometric patterns), mosaics, brick walls.
• ➕ Key Properties: Shapes must completely cover a surface. Angles around each vertex must add up to $360^{\circ}$.

🧪 Practice Quiz

1. Which of the following is a common example of a tessellation found in nature?

   1. A. Spider web
   2. B. Bird feathers
   3. C. Honeycomb
   4. D. Tree bark

2. What is the defining characteristic of a regular tessellation?

   1. A. It uses irregular polygons.
   2. B. It has gaps between shapes.
   3. C. It uses only one type of regular polygon.
   4. D. It overlaps shapes.

3. Which of these shapes CANNOT be used to create a regular tessellation on its own?

   1. A. Equilateral triangle
   2. B. Square
   3. C. Regular pentagon
   4. D. Regular hexagon

4. Where are tessellations commonly found in architecture?

   1. A. In the design of skyscrapers
   2. B. In Islamic art and mosaics
   3. C. In suspension bridges
   4. D. In geodesic domes

5. What is the minimum number of different regular polygons required to create a semi-regular tessellation?

   1. A. One
   2. B. Two
   3. C. Three
   4. D. Four

6. Which of the following is NOT a key property of tessellations?

   1. A. Shapes must completely cover a surface.
   2. B. Angles around each vertex must add up to $360^{\circ}$.
   3. C. Shapes must be the same color.
   4. D. There should be no gaps or overlaps.

7. Which of these structures commonly uses tessellations for its walls?

   1. A. Log cabins
   2. B. Brick buildings
   3. C. Igloos
   4. D. Tents