Dodecatiling

Probably mostly pictures this post.

On twitter and their blogs, Daniel Ruiz Aguilera and Simon Gregg have been pattern block crazy. Daniel recently did a very cool class and a presentation about it (see more) and Simon is always breaking reality with his students and pattern blocks.

Simon:

So Daniel tweets:

 

Edmund answers:

 

And then I got wondering about a tile with maximal dodecahedrons. I really liked the result of four 90^o rotations. 

But I was having trouble extending it using the pattern blocks. So I fired up GeoGebra and starting playing with the regular polyhedron tool, and came up with a pattern I liked. If felt like 2x4 rectangles of dodecahedrons, that had the rotating 4 block in the middle, and met in a rotating four block.

  

That left the gap to figure out. Here is the pattern with the gap (fill in how you want). [Math Toybox is the site I used to play with the blocks. Not the satisfying click of wood, but I love the save feature!]

Here's how I filled in the gap. I had blue rhombs where the triangles matched up, but that blurred the lines of the dodecahedrons. And I wanted it to look like it was overlapping. (On Math Toybox.)

This was a little maddening, but also fun. By the end these arrangements just made a deep kind of sense and I could see the pattern and replicate it easily - definitely not the case at the beginning. So thanks/gracias/merci to Simon and Daniel.