
As a math topic I just love them. The visual aspect, the geometry, the connections with algebra, the historical context, the art connections with Escher... it's darn near perfect. Working with 2nd - 12th graders they are amazing for rigid motions because you use the motions to make the tiles, then to repeat the tiles in a pattern, then can see the motions in the finished tessellation. It's visual and kinesthetic. There ought to be a song.
Instead, how about some geogebra. For some reason, this time around, I got interested in kites. Which tessellate by side to side rotation and what would a mixed glide reflection/rotation tessellation look like.

Webpage or geogebra file.

This sketch lets you make alterations to that classic 60-120-90-90 kite tiling. The sketch will adjust and give you a chance to both design and watch the effects.
Webpage or geogebra file.
This sketch does a tiling that can be done with any kite. (Pretty good question as to why it works for any kite!) Two of the congruent sides rotate to themselves around a midpoint, and the other two fit together with a glide reflection. Escher was fond of this pattern, as it allowed him to create creatures going in opposite directions for his contrasting tilings.
Webpage or geogebra file.
I would love to hear from readers if they prefer these geogebra sketches as links or embedded applets. Could you take a second to comment? Also, I love making geogebra tessellations, so if you have any ideas for ones you'd like to see, let me know.
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