News and Events

Keep up to date with Steve Nurse's designs and 3d printing.

Monday, 13 June 2022

Edge nets for polyhedra continued


 

1. Pattern from my first post on this subject. It shows a continuous loop, of a form that can make a tetrahedron like shape. There are 4 triangular nodes, and 3 edges with cane crossings, and 3 without.
   


2. I wanted to make the shape shown in 1. in 3d from cane but didn't think I could with the jigs I had previously. What was built along these lines previously was a 4 loop version of the same part, and I used 4 discrete jigs for that. This pic shows the revised jig, * The previous jig design was changed, so that there is now an 8mm central hole, * A central jig was designed and made, so that 8mm allthread rod fits into 4 sockets. * 8mm allthread rod was added, the outer rods ends are at the corner points of a tetrahedron. * Lastly, the new black jigs were bolted securely in place. 

3. Then starting with some cane poking into thin air, the cane was pressed into the black jigs and clipped in place. I made 3 crossing edges and 3 that didn't cross.

4. I needed to lengthen the cane a bit, so added an "invisible" join from clear heat shrink, but besides that, the whole thing can be made in 1 loop with 1 start / end join. In this photo, the loop is ready for gluing so the jig can be removed, and it looks like

5. This!

6. Here it is again. The jig makes a nice stand for the cane loop, as the corner sits snugly in place without glueing or clamping.


Hi. More 3d printing and weaving! Regards Steve Nurse

Update June 15.

When I started looking at the cane weaving I had made, (5 and 6) I started wondering what sort of polyhedron I had made. The 4 loop version ( 19 to 22 here) was a cuboctahedron, what is the one loop version? As answer of sorts I made some diagrams this morning, some highly modified versions of pic 1 above with different colours representing triangles, rectangles and pentagons (topology, not the actual number of sides). They are shown on 7 and 8.

There are lots of different ways of changing the number of loops in the basic cuboctahedron, and I thought of a couple that would preserve symmetry and sketched them by hand, and as per 9a and b below. Plan to make these at some stage. Also make more diagrams as per 7 and 8. 

Regards

7.


8.


9.

Update 17/6/2022

10. is the same thing as 9a

11. is the same thing as 9b


12. I wanted to explain the type of pic I made in 7, 8. 10, 11, where the outside border of the paper "doesn't count as sides". I was trying for a flat part printed both sides. "A" is the start, the same as fig 7 above and fig 10 on this page. "B" starts to divide it up, inside the hexagon will go to one side of the paper, outside the hexagon will go on the other.

13. Here, "A" is starting to construct the shape that will go on side 1, "B" is the finished side 1 construction and "C" is side 2.

14. Finished result. Blue = topologically 3 sided, red = topologically 4 sided. Some extra tabs were added to make the final form,

15. Which is here

16. and here. I didn't have to fold it flat, I manged to tape edges together to make a 3d shape.


Tuesday, 24 May 2022

Braided Knitted Ball / Edge Nets for Polyhedra

 Hi

After making a paper tetrahedron (see my last post), I have kept on working on polyhedrons which follow Marleen Hartog's pattern for a braided knitted ball.  So I have made considerable progress, and have been able to work out along the way some of the theory and principles of what I've been doing. 

So from the last post, I had made a paper cube as per Marlene's instructions, and had made a cane version (figure 9), and also managed to make some paper tetrahedrons. The tetrahedrons had one paper loop per side, with the paper loop completely surrounding each face, and an over and under pattern at each corner. The corners end up being mostly flat, and the assembled versions mostly spherical.


Starting with the pattern criteria that an octahedron has 4 edges at each corner, I started drawing an octahedron net based on what I'd done with the tetrahedron. The octahedron is more complex than the tetrahedron, and I took a simpler approach to making it this time, just putting different colours on white paper instead of printing outlines on different coloured sheets of paper.

So I think I've made a few "edge nets" here. The geometry nets I've heard of consist of full faces joined at hinging edges and accurately reproduce polyhedra. The joins between faces are the edges, and these are either joined like hinges "inside the pattern", or are split edges "outside the pattern". Pairs of split edges combine and coincide when polyhedra are made from nets.

The edge nets I've made consist of edges made of 2 distinct areas / struts and "roundabout" or over / under / over intersections for corners. There is nothing at actual corner points as they are at the centre of the roundabouts. A result of the 2-struts-per-edge feature is that given the correct nodes, an edge net can be made fully traversable, or made from one piece of cane. They have "two or no odd nodes" , a mathematical concept which I somehow remember from school, or engineering at uni. A long time ago!

So now I've managed to make all 5 platonic solids in this form. It makes the edge nets more complex than necessary, but also more versatile and mathematically- , and generally- interesting.

The dodecahedron was tricky and the icosahedron looked even trickier, until I realised that the edge polygons nets fit in the conventional nets of their dual. That means a cube net can be used as the basis of an octahedron edge net, and vice versa. The "rule" I used is that a dodecahedron net can be used as the basis of an icosahedron edge net and vice versa.

That is probably enough for one blog post, I will add in the pictures now. Drawings were made from scratch in Draftsight, other materials are printing ink, paper sticky tape and lamination sleeves. I plan to make a few more cane structures next, starting with the tetrahedron.


 

1)  3 tetrahedrons

2) Tetrahedron edge net, makes the shape shown at the bottom of 1).










3) Conventional net for cube

4) Edge net for cube

5) Conventional and edge nets made into cubes


6) Octahedron edge net 1: colours surround each side, 8 loops

7) Octahedron edge net 2 with colours surrounding each half, 6 loops

8) Octahedrons

9) Conventional edge net for icosahedron made from the 3d printable construction kit available here. Playing with these helped me work out the icosahedron edge net.


10) Dodecahedron edge net

11) What it says!

12) Above pattern with icosahedron edge net overlaid

13) Icosahedron edge net



14) Dodecahedron, Icosahedron

15) Laminating after printing

16) Kerrie quite liked them, we gave her a few patterns to make


Update June 1, 2022

Over the last 2 days, I've made and started to use a new jig which holds basket cane in the right position to make a tetrahedron based on the patterns of figure 1 above. I managed to design and 3d print the jigs one night, (17) and use them to make a tetrahedron the next. 

The 2mm basket cane was soaked in water, then 1 ring was connected using heat shrink tube. The ring was then clipped into the bend jig (19) , and gradually more rings added. When all rings were in place and closed, I glued the rings together at the 3 crossing points of the nodes. When the glue was dry I removed the clips and jigs.

In the middle of last night I realised the photos of the finished shapes would look good on a white background without a flash, to show off the shadows, so got up and took a few photos in my pajamas, and they are shown below (20 - 22).  The end shape is like an inflated tetrahedron with chamfered edges (it is topologically a cuboctohedron )   More to follow.

17) 2d drawing printed out. 3d drawing and 3d printed jigs followed.


18) Jigs and clips

19) Jigs and clips in place while glue dries.

20) Et Voila! Much easier to see what's happening in 19!

21)

22)

Friday, 6 May 2022

Braided Knitted Ball

 

1)

2)

3)

4)

5)

6)

7)

8)

9) Form is similar to that of a Rhombicuboctahedron.

Hi


A few weeks ago, our friend Christine Durbridge came over after a summons from my wife Christine. 

Our niece in England was having a baby (who has since been born, welcome to the world, Ed!) and Christine wanted to sew some decorations on some singlets, and was after technical advice. Now for all things sewing and knitting, Christine D. is the guru.

So Christine came around and the discussion somehow got onto a knitted braided ball design which Christine somehow produced for us via the wonders of her ipad thingy (1, 2). 

So the pattern for this ball (3) has been hanging around our house for a while, and one day I got out scissors, stapler and coloured paper, and made the paper equivalent (4,5). This is suggested in the knitted ball instructions as a guide to final assembly. 

I wasn't quite satisfied with that! Questions such as "If this is a cube, what does the tetrahedron look like?" arose!

Anyway, as a sort-of answer, I have made a basket-cane topological equivalent of the paper cube (5 - 9), and it ends up being a type of chamfered octahedron or rhombicuboctahedron. To make it, I used 6 of the 4 rod glue jigs I already had designed and made, 3mm basket cane, fold back clips, superglue, electrical heat shrink, and a hot air gun.

After making 2 rings using a heat gun, cane and heat shrink, the rings are joined by 2 jigs and fold back clips. Then an extra 2 canes are added. The new canes are closed as rings once they have been woven and clipped in place. A final set of 2 canes is then added, then closed to become rings. With the jigs still in place, all 24 cane crossings were glued with superglue. Finally, all fold back clips and jigs are removed. The last step should be done within a few minutes of glueing, as jigs can get permanently stuck to cane if you wait longer. Et voila! (9)

What other shapes can be made in the same pattern, I don't know, I need more think-time.

Regards Steve Nurse

Update after a bit of think time. I came up with the 2d patterns below which are flattened,  chamfered tetrahedrons. By fiddling with the nodes, the pattern was "made" with 4 loops, 3 loops and 1 loop.

  I will have a go at making a cane version of 10 and report back.

Regards  Steve

 

10) 4 Loop tetrahedron

11) 3 loop tetrahedron with modified nodes

12) 1 loop tetrahedron with modified nodes

Update May 10, 2022

I drew a single path version of 12, with twists in the edges allowing the 6 edge tetrahedron to be made from a single strip of paper or a single piece of cane, and that is shown in 13. From then, with my wife Christine's help I made a paper 3d version of the tetrahedron plan shown in 10). The plan is shown in 14, the making of it in 15, and the results in 16, 17 and 18. It could be made from more colourful paper but otherwise I'm very happy. Will continue!

Regards Steve Nurse

13) 1 loop tetrahedron with nodes preserved and switches in edges to achieve the single loop.


14)

15)

16) A 3d version of 10)

17)

18)

Update, May 12, 2022

Today I made a new version of the paper ball shown in 18, and worked out I could use some A4 thin cardboard sheets I already had for it. Plus a new red sheet from Officeworks. Its come out much better. Might have one more go at this tetrahedron before trying the next (slightly more complicated) thing.