```
library(tidyverse)
library(interp)
x = c(runif(500), 0,0,1,1)
y = c(runif(500), 0,1,0,1)
triangles(tri.mesh(x = x,y = y)) |>
as_tibble() |>
mutate(i=1:n()) |>
rowwise() |>
mutate(tri = list(
tibble(x=x[c(node1,node2,node3,node1)],
y=y[c(node1,node2,node3,node1)]))) |>
unnest('tri') |>
ggplot() +
geom_polygon(aes(x=x,y=y,group=i,fill=i), show.legend=FALSE) +
scale_fill_viridis_c(option='F') +
theme_void()
```
A tridecagonal (13-gon) tiling of a 3-periodic infinite surface. (1/n) #TilingTuesday
Window, North Gate, Imperial Citadel of Thăng Long, Hanoi, Vietnam https://en.wikipedia.org/wiki/Imperial_Citadel_of_Th%C4%83ng_Long#North_Gate_(C%E1%BB%ADa_B%E1%BA%AFc,_or_B%E1%BA%AFc_M%C3%B4n)
#Tiling #TilingTuesday #Pattern #Geometry #MathArt #MathsArt #photography #architecture
Diagonal 
section of ðe 4d cartesian product of 2 "I want to be a sea urchin and eat cabbage"(yes, really) tilings
kinda like ðis
Unfortunately we are still too dimensionally, perceptually, & probably intellectually challenged to even try to look at ðe full θing 
Back to #KnightPolygons (polygons formed by (2,1)-moves), here is a pair of tilings I did back c. 2020, using a knight polygon I dub the "Swan".
Two tilings of tangent circles for #TilingTuesday .
#MathArt #tiling #Mathematics
The 2- and 3-ominoes with diagonal stripes passing through the midpoints of cell edges have area 25, and can tile a 5×5 square. This was pleasing to solve manually, and could make a good lasercut acrylic puzzle.
@katherine_montalto this is a #TilingTuesday friendly post:)
#TilingTuesday 2d cross-section of an 8d point arrangement in ðe hypercubic honeycomb, wiθ 1 point at ðe center of each non-vertex facet & a sphere 10^-5 times ðe radius at ðe center of each 8-cube 𓅱
And for #TilingTuesday this simple #tiling with ellipse arcs.
#MathArt #Mathematics
There are 12 ways to replace two of the cells of an L tetromino with diagonal bars of opposite orientations. They form a unique 6×6 square tiling with a single cycle of overlapping perpendicular bars up to the symmetries of the square and swapping the bar orientations.
Net found for early #TilingTuesday
Fun way to create 2d tilings
http://www.paulbourke.net/geometry/2d3dtiles/
There are 18 hexominoes that can be traversed with orthogonal moves without revisiting cells. This tiling has a closed tour, where all of the cells in each hexomino are visited in an uninterrupted sequence. (I have a blog post in the works about this stuff, but it's not quite done, and Tuesday very nearly is.)
