From Math Images
Tessellation's are an interesting topic, one that many people find very approachable.
In your discussion on regular polygon patterns, there is a mistake in your discussion of triangles, many triangles work in tessellation's, equilateral triangles just happen to be a regular triangle.
When speaking of the irregular polygon tessellation, it would be interesting to show the tessellation, maybe with a graphic that outlines the shape being tessellated.
You could add a lot of interest by showing how to construct a tessellation.