If you look at the rules above, only rule 2 changes slightly for semi-regular tessellations. If you use a combination of more than one regular polygon to tile the plane, then it's called a "semi-regular" tessellation. The mathematics to explain this is a little complicated, so we won't look at it here ![]() So what's unique to those 3 shapes (triangle, square and hexagon)? As it turns out, the key here is that the internal angles of each of these three is an exact divisor of 360 (internal angle of triangle is 60, that of square is 90, and for a hexagon is 120). You can see that there is a gap and that's not allowed. Let's try with pentagons and see what shape we come up with. You may wonder why other shapes won't work. Let me show you examples of these two here. What are the other two? They are triangles and hexagons. Of course, you would have guessed that one is a square.
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