Truncated Octahedron Corrugator

This is my attempt at creating something that is like corrugated cardboard, but a bit stronger, where the surface profile of the corrugations forms a truncated octahedron surface, rather than a sine wave or triangular wave.

It doesn't have to be cardboard; this process should be applicable for any thin surface. The surface can be created by any means that creates the end product.

To make the corrugated cardboard:

1. cut up three thin strips of card and paper (a Sunlight soap box is pictured)

2. put one strip into the rollers

3. make up a flour paste (mix flour and water to make a paste with the consistency of gravy)

4. apply the paste to one side of a flat strip, then stick the strip to one side of the corrugated strip

5. apply the paste to one side of a flat strip, then stick the strip to the other side of the corrugated strip

6. Heat in an oven at 50°C for 10-15 minutes, or place each side on a 50°C heated print bed for 10-15 minutes.

My initial goal is to make a roller that can create corrugations for an A4-sized sheet of paper, i.e. where the roller width is 210mm. That will make it easy to create a demonstrable product, because A4 paper is plentiful.

Here is my attempt at more formally explaining possible variations:

1. A method for creating a thin structure (or skin) that has a profile matching the surface of a truncated octahedron tiling.

2. The method in claim 1, where the surface profile matches a linearly-transformed representation of a truncated octahedron tiling.

3. The method in claim 1, where the surface profile matches a continuously-transformed representation of a truncated octahedron tiling.

4. The method in claim 1, where the surface profile matches an arbitrarily-transformed representation of a truncated octahedron tiling.

5. The method in claim 3, where the surface that the tiling is mapped to has a cylindrical structure.

6. The method in claim 3, where the surface that the tiling is mapped to has a spherical structure.

7. The method in claim 4, where the surface that the tiling is mapped to is an arbitrarily curved surface.

8. The method in claim 4, where the surface that the tiling is mapped to is an arbitrarily shaped surface.

9. The method in claim 8, where the thin structure is created by pressing two solid objects together onto opposing sides of a thin surface with high pressure, with each of the objects having a surface profile matching an arbitrarily-transformed representation of a truncated octahedron tiling.

10. The method in claim 2, where the thin structure is created by a cylindrical geared mechanism, where the cylinders have a surface profile matching a continuously-transformed representation of a truncated octahedron tiling.

11. The method in claim 2, where the thin structure is created by placing it on top of a linearly-transformed representation of a truncated octahedron tiling, and rolling a cylindrical form over the top of it, where the cylindrical form has a surface profile matching a continuously-transformed representation of a truncated octahedron tiling.

12. The method in claim 8, where the thin structure is created by layering a viscous substance onto a surface that has a surface profile matching an arbitrarily-transformed representation of a truncated octahedron tiling, where the viscous substance hardens over time.

13. The method in claim 12, where the viscous substance is injected into gaps between the surface and a paired surface, and the surfaces are subsequently separated from the thin structure after the structure has hardened enough to retain its shape.

14. The method in claim 8, where the thin structure is created by extruding a viscous substance that hardens over time.

15. The method in claim 8, where the thin structure is created by hardening a liquid using electromagnetic radiation.

16. The method in claim 8, where the thin structure is created by fusing a powder using electromagnetic radiation.

17. The method in claim 15, where the thin structure is created by hardening a liquid using UV light.

18. The method in claim 16, where the thin structure is created by fusing a powder using a laser.

19. A method for creating a three-layered structure, where the central layer matches the thin structure described in claim 2, and the outer layers are planar surfaces that are fused to the central structure.

20. A method for creating a three-layered structure, where the central layer matches the thin structure described in claim 5, and the outer layers are cylindrical surfaces that are fused to the central structure.

21. A method for creating a multi-layered structure, where inner layers match the thin structure described in claim 2 and are fused to adjacent inner layers to leave voids that have a shape close to a truncated octahedron, and the outer layers are planar surfaces.

22. A method for creating a multi-layered structure, where inner layers match the thin structure described in claim 8 and are fused to adjacent inner layers, and the outer layers are arbitrarily-shaped surfaces.

More human-readable explanation:

• Claims 1-8: describe the surface structure itself, which should evoke the "feeling" of a tiled truncated octahedron structure due to being mapped appropriately to the surface of a base object

  • 1 - the fundamental object: a truncated octahedron skin

  • 2 - a squished, stretched, or rotated version of the truncated octahedron skin

  • 3 - mapped to a regular shape (e.g. see my other models)

  • 4 - mapped to an arbitrary surface... somehow

  • 5 - mapped specifically to a cylinder

  • 6 - mapped specifically to a sphere

  • 7 - mapped to an arbitrary curved surface (e.g. a smoothed landscape)

  • 8 - mapped to an arbitrary surface (e.g. a box)

• Claims 9-18: describe possible ways in which the surface structure can be created

  • 9 - form / press / high pressure

  • 10 - between rollers (as in the first prototype example)

  • 11 - rolling a cylinder on top of a surface (a bit like a pizza cutter)

  • 12 - open mould (e.g. concrete spray)

  • 13 - injection molding

  • 14 - FDM 3D printing

  • 15 - SLA 3D printing

  • 16 - SLS 3D printing

  • 17 - SLA (specifically using UV light)

  • 18 - SLS (specifically using a laser to melt/fuse stuff)

• Claims 19-22: describe how a flat support structure can be created that uses the structural benefit of the truncated octahedron tiling

  • 19 - the closest approximation to flat corrugated cardboard

  • 20 - like cylindrical corrugated cardboard

  • 21 - like multi-layered corrugated cardboard, but without intermediate flat layers

  • 22 - multi-layered support structure with an arbitrary outer surface