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Gyroid, Quadrangular Tile 60, Quad_60

3d0dd15e-f147-4089-a400-71425512d62d.png Gyroid, Quadrangular Tile 60, Quad_60
98e9044f-5f09-4022-9b59-1b2cc0965755.png Gyroid, Quadrangular Tile 60, Quad_60
4ef70ff8-2b42-4bba-a1d0-4deca0754b89.png Gyroid, Quadrangular Tile 60, Quad_60
a8389272-0d42-4dab-b561-6c45531a0b66.png Gyroid, Quadrangular Tile 60, Quad_60
b665f3a4-41e0-4b7c-93db-062b4d2336b3.png Gyroid, Quadrangular Tile 60, Quad_60
1bd73149-f3d3-4dd5-a04d-b2db9b1cbf99.png Gyroid, Quadrangular Tile 60, Quad_60
f0196592-62ae-4685-bc13-34c5581e2870.png Gyroid, Quadrangular Tile 60, Quad_60
a635e70e-64da-4e80-b40c-8e173ba8849e.png Gyroid, Quadrangular Tile 60, Quad_60
Quad60-Single.stl Gyroid, Quadrangular Tile 60, Quad_60
Quad60-Single-Support.stl Gyroid, Quadrangular Tile 60, Quad_60
Quad60x6.stl Gyroid, Quadrangular Tile 60, Quad_60
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  • Quad60-Single-Support.stl
  • Quad60-Single.stl
  • Quad60x6.stl

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Publication date 2024-01-16 at 00:02
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Published to Thingiverse on: 2024-01-15 at 18:05
Design number 1715373
LGBU

LGBU

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3D model description

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 .

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