1d to 3d part 2

 

1. Original purpose for jig: irregular hex structure makes converging pairs.

2. Hijacked for a different purpose: diverging pairs.

3. And a third possibility: radial pairs.

4. The 3 parts from the 19 degree angle jig highlighting mismatch.

5. Parts from the 20 degree jig - The converging pair model still has sticks converging at a point, and the other 2 models are now compatible.

6. Maths showing how the 20 degree configuration works. For compatibility B = C, see also pic 13 for diagrams of shapes.

7. Last night's inspiration: Vertex connected tetrahedron, sides have a regular hexagon as the structure at the centre.

8. Tetrahedron from 7, and a vertex connected tetrahedron with mixed sides, 2 as per 2 and 2 as per 3. 

9. Side connected tetrahedron, diverging sides

10. Side connected tetrahedron, radial sides.

11. Side connected tetrahedron, sides are a mix of pics 2 and 3.

12. Alternate view of 9.

13. Centreline sketches of items 1, 2 and 3, and compiled view used to work out geometry. Sizes from central sketch were used to design the jig MKII.

Hi

Since my last post, I have been progressing quite well, making mostly abstract structures from  coffee stirrers and segments of drinking straws. I've posted on my instagram more often than blogging, so if you want to catch up a bit then head on over there.

But some new developments seemed quite interesting, and I wanted to write in a longer form than insta allows.  I had 3d printed and used a few different jigs to make sides for polyhedra, but had generally only made one type of shape per jig. Then a few nights ago I started exploring, making radially symmetric parts for example. 

Soon after developing a range of parts (pics 1, 2, 3) that could come from an irregular hexagon jig, I realised that with a bit of tweaking, 2 of the parts could be compatible in structures. Not only that, they could be put together in 2 ways (edge connected and vertex connected) in all the platonic solids that have triangles as faces, that is tetrahedrons, octahedrons and icosahedrons.

Sofar I have just made tetrahedrons in this specific way, and a few samples are shown above.

The tweakage to get the type 2 and 3 sides to be compatible was changing the angle between coinciding sticks (type 1) to 20 degrees form 19. 20 degrees is exactly right and I stumbled on this angle by guesswork but later proved it to be correct with a surprisingly simple method I am very proud of (pics 6 and 13).

Not sure what I'll build next and I hope you enjoyed this slightly longer form of description.

Regards

 

Steve Nurse