STUDENT EXAMPLES|
A tessellation is a way to tile a floor (that goes on forever) with shapes so that there is no overlapping & no gaps. A puzzle is a tessellation! The shapes were weird.
REGULAR TESSELLATIONS:
What can we tessellate using these rules? Triangles? Yep! Notice what happens at each vertex! The interior angle of each
equilateral triangle is
What happens at each vertex? 90 + 90 + 90 + 90 = 360 degrees again! So, we need to use regular polygons that add up to 360 degrees. Will pentagons work? The interior angle of a pentagon is 108 degrees. . . 108 + 108 + 108 = 324 degrees . . . Nope!
Hexagons? 120 + 120 + 120 = 360 degrees Yep! Heptagons? No way!! Now we are getting overlaps!
Octagons? Nope! They'll overlap too. In fact, all polygons with more than six sides will overlap! So, the only regular polygons that tessellate are triangles, squares and hexagons! SEMI-REGULAR TESSELLATIONS:These tessellations are made by using two or more different regular polygons. The rules are still the same. Every vertex must have the exact same configuration.
These tessellations are both made up of hexagons and triangles, but their vertex configuration is different. That's why we've named them! To name a tessellation, simply work your way around one vertex counting the number of sides of the polygons that form that vertex. The trick is to go around the vertex in order so that the smallest numbers possible appear first. That's why we wouldn't call our 3, 3, 3, 3, 6 tessellation a 3, 3, 6, 3, 3! Here's another tessellation made up of hexagons and triangles. Can you see why this isn't an official semi-regular tessellation?  It breaks the vertex rule! Do you see where? Here are some tessellations using squares and triangles:
Can you see why this one won't be a semi-regular tessellation?
MORE SEMI-REGULAR TESSELLATIONS
What other semi-regular tessellations can you think of? 
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