It's the
#mathphoto15 summer challenge on Twitter and it's
tessellations week. There have been lots of great tiling patterns shared already, and it's been really interesting because we inevitably stretch the definition of what a tessellation is. Does there have to be traslational regularity? Can a tiling have a centre? Does it have to be regular even? Do there have to be a finite number of different tiles? Do they have to be on a flat surface?
It's just the week for me, and my favourite tool for exploring tiles is pattern blocks, so I returned to
some earlier thoughts I'd had, and a particular pattern.
But of course I wanted to share the week with my class a little. So I showed them this and talked about some of the different kinds of tilings you might get. Then I asked them for some of their own. With a constraint. It's usually good to give a constraint. ("Can you make a pattern without a centre?" is a good one; our first impulse is to build out from a centre.) This time the constraint was to use the same three tiles. So here's some of their ideas:

Interesting how they've taken it round a corner. Will this work? 

Samyak thought there wouldn't be any more hexagons in this one. 

This one was the most interesting to me, but its creators, Marie and Rose
thought it wasn't regular enough! 
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