Snub Square Tiling

by Tuğrul Yazar | October 22, 2012 14:45

This was the first step in the generation of Cairo Pentagonal Tiling. It is the dual of a semi-regular tiling of the snub square.

The first step was easy. Just dispatch cells of a square grid, then evaluate them according to the ratio of 0.366 approx. which is derived from the bisector of an equilateral triangle. Here is the definition:  [GHX: 0.9.0014][1] Now, we have a snub square tiling, composed of tilted squares, but in order to process it further and explore different potentials, I had to tell Grasshopper about the equal triangles also. So that made the definition a little bit more crowded because I had to connect proper vertex IDs of different grid cells and join them together to emerge new shapes:

This is much prettier but a little complex. Here is the definition [GHX: 0.9.0014][2]

[3]

Then, I played with these vertices to produce the following results. Note that these definitions may easily be conformed onto any surface as we did before.

To create the above tiling, just turn off all except the 4 polyline components in the middle. I’ll continue with Cairo Pentagonal Tiling.

Endnotes:
  1. [GHX: 0.9.0014]: https://www.designcoding.net/decoder/wp-content/uploads/2012/10/2012_10_22-snub1.ghx
  2. [GHX: 0.9.0014]: https://www.designcoding.net/decoder/wp-content/uploads/2012/10/2012_10_22-snub2.ghx
  3. [Image]: https://www.designcoding.net/decoder/wp-content/uploads/2012/10/2012_10_22-snub2-def.jpg

Source URL: https://www.designcoding.net/snub-square-tiling/