Here's a variation on polytans. Start with a unit tan as usual, but in addition to joining another unit tan to it, you can join the leg of a larger tan to the hypotenuse of a previous tan. There are 14 subtiled tri-inflatable-tans, and the set can tile a 5×6 rectangle. I played with it manually, and it feels like a good manual puzzle. For a bit of extra challenge, I looked for a solution where all of the interior long edges between pieces (length 2 or 2√2) join edge to edge, and one where none of them do. These are below.
It's #TilingTuesday! Here's a tiling around a seed, consisting of a hexagon with pentagons at each side. The overlapping 24-gons are not quite regular.
⚠️NEW SHAPE ALERT⚠️
"Mixed nuts" tiling, made from regular 15/10/3gons(yes, ðose fit exactly around a vertex), rhombs, & some 12/6gons ðat alternate 2 angles(ðey could also be replaced by clusters of ðe oðer shapes)
Today's #TilingTuesday is also a #TapestryTuesday.
The cushion cover on this piano stool was designed and stitched by my grandfather circa 1983. He made similar cushion covers for all his dining chairs. Each cover had a different geometric pattern but they were all stitched in the same colours.
I remember him using large sheets of graph paper to plan the designs. This was probably my first introduction to #MathArt, long before I knew that #MathArt was a thing.
Much thanks to @domotorp and Renan Gross for tracking down the key result the post needed. The graphic below is a 142-omino with no 4 equally spaced cells on the same line, proved maximal by Jan Kristian Haugland.
#tilingtuesday
Created in Tilemaker for Android
I'd love to create some patterns using only straight lines but the Tilemaker app insists that I include some circles and I haven't yet found a better app.