Gyroid, Quadrangular Tile 60, Quad_60

Quadrangular Tile 60, Quad_60, of the Gyroid

Quad 60 Tiles the Gyroid Surface

The gyroid can be constructed using several component surfaces in 3D tessellation, taking advantage of its intrinsic symmetries. Schoen illustrated the * quadrangular tile* or Quad-60 in Figure 3.3i-j-k on https://schoengeometry.com/e-tpms.html . The quad-60 tile is easier to print with minimal support. Six copies of Quad-60 will make a "semi-regular skew 12-gon" with face angles at alternating 60 and 120 degrees. Schoen mentioned that this 12-gon does not tile G. However, in my experiments, it seems that it does with rotation and reflection. I have yet to find a physical counterexample. I will post an update when I do have one ready.

That said, the 12-gon is not easy to print because it requires extensive support. So it is recommended that quad 60 be used to tile the G, using the 12-gon as an experimental intermediate component.

Reference

https://schoengeometry.com/e-tpms.html, Figures E3.3i-l .