Tessellations Using Two or More Shapes
Tiling
Task: Use at least two different regular shapes to create a tessellation pattern that covers the grid below perfectly. Be creative.
Note: Do note resize the shapes. The shapes should have matching side lengths.
Evaluation: The 360° Audit
- The motif check: Can you find the repeating pattern? Does it look like a single tile or a cluster of shapes?
- The isometry test: How was the pattern replicated? Did the motif translate / rotate / reflect / glide reflect? The pattern is considered a tessellation if these movements can continue infinitely in all directions to cover the surface.
- The 360° rule check: Look for the vertex. For shapes to lie flat without gaps or overlaps, the sum of the interior angles meeting at that point must be exactly 360°.
The 8 Semi-regular Tessellations
Goal: Identify and categorise the 8 specific semi-regular tessellations.
A Semi-regular Tessellation must meet two criteria:
- It uses two or more different regular polygons.
- The arrangement of polygons at every vertex must be identical.
Homogeneous vs. Non-homogeneous Semi-regular Tessellations
*Review Concept: Tessellation refers to the process of covering a surface with repeating shapes in such a way that there are no gaps or overlaps, and the interior angles of the polygons meeting at a vertex must be exactly totaled 360°.
Homogeneous Tessellations:
- The pattern uses the same congruent shape(s) arranged in the same order / configuration around every vertex.
- Can be in the form of regular (uses only 1 type of regular polygon) and semi-regular (uses at least two types of regular polygon) tessellation.
- All polygons in the motif must meet at its vertex (edge-to-edge).
- Every vertex in the tiling must be identical. The same shapes must meet in the same circular order at every vertex / meeting point.
Non-homogeneous Tessellations:
- The arrangement of shapes do not require the same order around every vertex.
- Can be in the form of irregular shapes or a combination of different shapes.
- This course focuses on non-homogeneous tessellations using only regular polygons.
- Composed of two or more types of regular polygons.
- All polygons in the motif must meet at its vertex (edge-to-edge).
- There are at two or more different types of arrangement used throughout the pattern.
- Each arrangement must meet at its respective vertex.