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#tilingtuesday

10 posts9 participants1 post today

A monohedral heptagonal tiling of an infinite surface, which I suspect to be related to the gyroid, but with different sized necks.
I am going to try to build this one tile by tile, and had forgotten how hard it is to deal with even the simplest of necessities like thickness. So a shout out to people who actually build stuff in the real world. (1/2)
#TilingTuesday

There are 18 ways (up to plane symmetries but not color swapping) to connect two pairs of edges on a triangle tetriamond with curves of different colors. 18 is a good number because it lets us tile a rhombus shaped fundamental domain. (I added the little black hexagons to highlight the underlying pattern of the repeats.

But then the problem is to make meaningful use of the colors, and I failed. It's nice to have all of the segments make one loop. This can't be achieved with alternating segment colors. My next thought was two consecutive segments of one color alternating with two of the other. I couldn't get there though.