In the news on Wikipedia:

Mathematicians at the University of Washington Bothell discover a new type of pentagon tiling (pictured), the first new way to "tile the plane" with a single polygon since 1985.

https://en.wikipedia.org/wiki/Pentagonal_tiling

 

Very interesting. I wonder how they come up with these things?

 

They'll have to use smaller words for me.

 

Pentagonal tiling huh?

Glad to know I have another option for retiling my shower!!!

 

Tiling can actually be an interesting challenge. I was having a large room tiled using using three tiles with different dimensions to give it a sort of "random" look. But it was anything but random. I had used a drawing program to work out the precise arrangement that would give a satisfying repeating unit using a combination of the 3 tiles. The appropriate number of all 3 tiles were ordered and the tile mason arrived. We then discovered that one of the shapes was ~1/8" less than the nominal dimension I had used for the drawing. This meant that I would have uneven grout lines if I had stuck with the original layout.

The tile mason was ready to head home. But using my computer I was able in minutes to reconfigure the layout to once again have uniform grout lines and a pleasingly "random" pattern. His jaw dropped but he did the job and it looked great. I'm not sure I convinced him to start using computerized layout, but he had to at least consider it.

 

Tiling can actually be an interesting challenge. I was having a large room tiled using using three tiles with different dimensions to give it a sort of "random" look. But it was anything but random. I had used a drawing program to work out the precise arrangement that would give a satisfying repeating unit using a combination of the 3 tiles. The appropriate number of all 3 tiles were ordered and the tile mason arrived. We then discovered that one of the shapes was ~1/8" less than the nominal dimension I had used for the drawing. This meant that I would have uneven grout lines if I had stuck with the original layout.

The tile mason was ready to head home. But using my computer I was able in minutes to reconfigure the layout to once again have uniform grout lines and a pleasingly "random" pattern. His jaw dropped but he did the job and it looked great. I'm not sure I convinced him to start using computerized layout, but he had to at least consider it.

That sounds like good drawing software. What was the name of it?

 

Hmmm, it was a while ago. I think it was Freehand. This was an excellent postscript drawing program for Mac. It was eventually bought by Adobe and then killed, so they could sell their Illustrator instead. But they never matched the features that Freehand users had come to love.

Anyway, the key is vector drawing at device-independent scale. There are other choices for this. I'm currently using Intaglio, which is an inexpensive option that is darn good.