isaackuo, 1 month ago

... The valid positions are either all even coordinates or all odd coordinates.

So, your graph paper has a scale of 2 for each line. You can either be on an intersection (all even coordinates) or on a square center (all odd coordinates).

Either way, movement is intuitive. Either move 2 in an orthogonal direction, or (1,1,1) in a diagonal direction.

I'd say this all compares favorably with the better known rhombic dodecahedron tiling.

#tabletop

2/2

johncarlosbaez, 1 month ago

@isaackuo - what a conincidence! This week my friend Mike Fourman has been using a 3d printer to create truncated octahedra, then using these to tile space. They're really cute.

EdS, 1 month ago

Another nice trick is to delete all the squares from this tiling of space, leaving you with a nice two-sided surface sometimes called the muoctahedron (I think.)

https://en.wikipedia.org/wiki/File:Petrie-2.gif

When I "discovered" this playing with Polydron pieces I was delighted. I had a feeling I've seen it called a Plumbers Nightmare but that may be something else.

I imagine this surface could be good for heat exchangers, or capacitors, or batteries.

@johncarlosbaez @isaackuo

johncarlosbaez, 1 month ago

@EdS @isaackuo - my friend Mike Fourman is using a 3d printer to print gyroids for heat exchangers.

https://mathworld.wolfram.com/Gyroid.html