Gyroid, Quadrangular Tile 60, Quad_60

thingiverse

Quadrangular Tile 60, Quad_60, of the GyroidQuad 60 Tiles the Gyroid SurfaceThe 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. Referencehttps://schoengeometry.com/e-tpms.html, Figures E3.3i-l .