Lmst

Another 18 heptagonal tiles. This is going to take a long time! #TilingTuesday #3dprinting #geometry

#TilingTuesday

A bunch of lines drawn on a colored background

Happy Escher's Birthday, happy #tilingtuesday !

#WorldTessellationDay
#TilingTuesday
Created at https://tiled.art/en/create/

More cairo animals. Here the base cairo tiles had the sides curved.
#TilingTuesday #CairoTiling #mathart #tiling #art

A tiling of ducks. They come in two versions: one white with yellow beaks and feet, and the other with green heads, two shades of brown body and orange beaks and feet. Two ducks are detached from the tiling near bottom left and right corners.

🐝

#TilingTuesday #dejavu #tiling #mastoart #abstract #geometry

A tiling of triangles hexagons realized with #neocube (small, spherical magnets) for #TilingTuesday

Second image highlights the tiling a bit better.

Third image shows the way the magnets were wound to produce the tiling (: (And also, how I imagine the magnets are oriented, north/south-wise, but I honestly need to find a way to simulate those instead of drawing them)

A hexagon of small ball bearing-sized magnets. The magnets are grouped into smaller triangles and larger hexagons that together make up the overall hexagon.

Last picture, this time overlaid with semi-transparent triangles and hexagons that highlight each of the groups of magnets.

Image of the ball bearing-like magnets again, this time overlaid with yellow clockwise spirals over each of the hexagons and purple counterclockwise spirals over each of the triangles. The magnets themselves have been covered by circles filled with a gradient from red on one end to cyan on the other.

Animated #TilingTuesday 🙂

Mudéjar exterior wall, Cathedral of the Savior (La Seo de Zaragoza), Zaragoza, Spain

“The long-standing rivalry between the canons of El Pilar and of La Seo was well known in the 17th century. ...[In] 1676, Pope Clement X made the Solomon-like decision to merge the two chapters via the Bull of Union. 6 prebendaries and 15 canons would reside in La Seo, and the same in El Pilar, and the dean would live 6 months in each one.” https://en.wikipedia.org/wiki/Cathedral_of_the_Savior_of_Zaragoza

#TilingTuesday #Mudejar #IslamicPattern #Gothic #church #geometry #tiling #MathArt #photography #architecture #history

Detail of an ornate wall made of pale brown bricks and blue and turquoise tiles. The bricks make raised curvilinear lines. Inside the shapes formed are blue and green eight-pointed stars and circular bowl-like shapes.
The overall effect is serene with mirror symmetry and some rotational symmetry.

for #tilingtuesday

UltraFractal6 DucksJ Lyapunov

$fractal image in warm yellows and whites. Repeating wavy woven patterns radiating from an upper central point , a bit like a sunset/sunrise.$

3/3

The fact that @DaniLaura 's turtles consist of Cairo tiles inspired me to also provide a basic Cairo tiling.

Try it
- with the provided backgrounds,
- on a cube or on the flattened star (using the "bending" slider).

#TilingTuesday

A star (an unfolded cube) with a turtle tiling and a Cairo tiling overlay

2/3

Play with it in https://hcschuetz.github.io/polyhedron-star/dist/:
- Select the example "cube with turtles",
- Rotate and move the cube with your mouse or touch device.
- Unfold/fold the cube to a flat star and back with the "bending" slider.
- Change the grid from "quad diagonal" to "quad".
- Change the grid density.
- Switch the background to "turtles (4 colors)".

The 4-color tiling on a folded cube leads to proper turtle shapes but color mismatches along the cuts.

#TilingTuesday

Last week's #TilingTuesday contribution https://mathstodon.xyz/@DaniLaura/114658815682032097 by @DaniLaura had two kinds of symmetry centers: "four-heads points" and "four-feet points". Rotating around one of these points by 90° leaves the tiling unchanged, except for the coloring.

Thus the turtle tiling has the kind of rotational symmetry needed for cubes in my polyhedron-folding tool. So I added (simplified variants of) that tiling.

Notice that at the corners only 3 rather than 4 turtles meet.

1/3

Here are the single tiles for comparison. While the first tile has edges of almost similar length, the shortest and longest edge of the second tile differ by almost factor 4. (3/3) #TilingTuesday

The tiling is quite twisted as can be seen in these short animations (2/3) #TilingTuesday

Two combinatorially equivalent monohedral heptagonal tilings of a surface wrapping the diamond bond structure.
Or in other words, by merely adjusting the edge lengths of the single tile you can go from one to the other and change the proportion ofthe two volumes separated by the surface. (1/3) #TilingTuesday #math #geometry