# tessellations mathart mathsart rhombus tiling rstats mathematics generative tidyverse hyperbolic

The newest great discovery in tilings is already implemented in HyperRogue. So you can play infinite aperiodic Minesweeper on it, or whatever!

89 778
2023-03-24

Here’s an interesting finding. It’s well-known that there are three pentagonal tilings which are duals of the Archimedean tilings, named Cairo, Prismatic, and Floret. Cairo and Prismatic are known to tile as a mixture. But what about all three? I can't find it in the literature.

5 39
2022-07-12

Third one is "Geometric realms" by

Persian tone and geometrical tilings??? these touches every single architect bone in my body

https://t.co/nLkO18efty

1 5
2022-05-09

In her talk Doris Schattschneider shared the link to the web app "[John H.] Conway's Magic Pen," which allows you to generate various tilings such as this one. She was the mathematical consultant behind it. https://t.co/yNBrgSXYWI

0 6
2021-10-22

One of my Escher-like tilings used to illustrate a spiral principle in a joint paper headed by Peichang Ouyang, an advanced mathematician, in ‘Generation of advanced Escher-like spiral tessellations’. The paper is open access: https://t.co/ikFs0KAKIb

9 26
2021-08-19

A glimpse of infinity.
Don't you just love nonperiodic tilings? They seem to have a mixture of order and disorder, poised at the edges of human intuition or comprehension. Source: https://t.co/LSkokHl0FI

11 78
2021-02-24

n-armed spiral tilings of trapezoids based on regular n-gons. When n = 4 the trapezoid becomes a rectangle. Note that n = 5 is unique in allowing two distinct ways of matching adjacent scaled tiles.

32 130
2021-02-19

Penrose tilings are examples of aperiodic tessellations – even though they only consist of a few different shapes, they never repeat themselves. https://t.co/IQKCeUTtvB

18 44
2020-06-18

Cool :3 maybe octilings? :D

0 4
2020-05-07

It finally works! I wrote a shadertoy that generates non-periodic tilings by taking 2d cross-sections of a 5d cubic grid! 🔪🧊

15 115
2020-03-02

The next version of the will support many more different shapes including dual polygons to create the duals of all uniform tilings.

https://t.co/nuknwbr2th

2 10
2019-05-13

Some images showing the multi-grid method for constructing rhombic tilings inside n-gons.

13 54
2019-03-15

Growing/shrinking a hyperbolic heptagon to yield a continuous transition between {7,3} and {7,27}

56 137
2019-02-04

Every tiling in the paper „Some Monohedral Tilings Derived From Regular Polygons“ by Paul Gailiunas can be drawn with the .

https://t.co/ZI7Qmchn6D

2 10
2019-01-22

Crescents tilings work also for even numbers of edges. But for 6 a chessboard coloring ist not always possible. But with 8 it works fine.

1 3
2019-01-13

I just added a number of eight-fold f-tilings to my fractal tilings website, some of which haven't been shown anywhere before. They're all single-prototile and edge-to-edge. See more at
https://t.co/Af0NENbrBc.

7 31
2018-08-29