1d to 3d part 3

 

1. Diagram for compact version

2. All the assemblies shown here were made on this jig

3. Compact tessellation

4. Corner connected tessellation from radial and diverging triangular units.

5. Edge connected tessellation from radial and diverging triangular units.

6. Edge connected octahedron from radial and diverging triangular units. Refer small ovtahedron, red - diverging, blue - radial.

7, Another view = Edge connected octahedron from radial and diverging triangular units. Refer small ovtahedron, red - diverging, blue - radial.

8. Corner connected octahedron from radial and diverging triangular units. Refer small octahedron, red - diverging, blue - radial.

9. Compact Octahedron

10. Compact Octahedron calcs

Hi 

Following on from my last post on this, I have worked on 6 piece sides made with an irregular hexagon jig (pic 2), introducing a new "compact" version where 4 stick ends allign along the edges of an equilateral triangle (pics 1, 3, 9, 10). The work includes making mixed (diverging and radial sided) octahedra of 2 types, drawing tessellations of 3 types, and calculating the geometry of the compact versions.  

I'm proud of this effort of drawing and calculation. When placed on the jig at stick centre position "X", the stick ends (modeled by their centrelines) assume heights H1 and H2 which can be calculated from the assumed stick length L = 172 and the jig / side geometry and the length "X". 

As a first step to getting the ends colinear, X is calculated for the colinear condition H1 = H2 = H.

With expressions for H1 and H2 which are equal, X can be found. Then by putting this X into expressions for either H1 or H2, H can be found. Calculated results for X and H match Cad results almost exactly. For maths purists, all the angles should be in radians, but I don't think it makes much sense here! For example, 10 degrees = PI / 18 radians, much more cumbersome! 

Novelty pencil airlines

 

When my friend and I were on our way home from my cousin's funeral last Friday and, we dropped in on a cemetery, one coffee shop and two Op Shops. We spent a while at the first Op Shop and I had perused the DVDs, CDs and perused and selected several books. My friend was going through all the dresses skirts and shoes, and wasn't done when I had just about seen everything I wanted to. But a bundle of pencils caught my eye they included novelty pencils with two rubbers on one end "HAMMER OUT YOU CLEANING NEEDS".

It wasn't till later when we had convened at the coffee shop later that we found out the bundle also included novelty pencils with a rubber at each end "THIS PENCIL WAS MADE ESPECIALLY FOR OUR COMPETITORS TO WRITE QUOTES” or “THIS PENCIL WAS MADE ESPECIALLY FOR OUR COMPETITORS TO WRITE NEW BUSINESS ". Of course I fiddled around with the pencils at the coffee shop trying to get them to stand up on their ends or balance them in some sort of tower. That night I passed a set of the pencils on to our friend Christine at her place over dinner. The next day I was busy but later while bored watching the TV (this was Saturday night) I started assembling the pencils together with a fold back clip and after a short amount of time came up with and aeroplane on a stand. 

This looked quite good but just needed a tail for the plane – I made one out of sticky tape (pic 1) but wasn’t satisfied. A few days later and a “proper” tail is complete along with a lame joke along the lines of what is written on the pencils. Cad pic made using Bricscad.

Regards Steve Nurse 

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.

 

Continues Here... 

Regards

 

Steve Nurse 

1d to 3d

Display at Bridges Eindhoven...

 

included this 1d to 3d dodecahedron

My setup on the opposite side of the hall.

Some art inspiration from England......

and from home. I took this photo to finish an article I have written.

Septagonal face in 3d printed jig.

Hexagonal and Pentagonal faces

Everything including a pentagonal face construction from spokes.

The flower shaped jig was a first off attempt, Bit of a problem there, the floback clip would need to be removed through the wooden assembly.

New materials

Soaking sticks for the 7 sided figure. Soaking makes them more pliable and so they can bend more without snapping.

Hi

Recently I attended the Bridges Maths and Arts conference in Eindhoven in the Netherlands. It was great and I will report further in other posts. But for now I'm reporting on some Bridges inspired stuff.

Next to the main Bridges conference hall was an informal poster area where I set up camp at a table to show and discuss some of my 3d printed things.  I was intrigued by some of the displays including one of (basically) one dimensional wooden blocks transformed into a dodecahedron. Unfortunately I didn't get the contact details of the gentleman who had made them. The work was made simpler by connecting the pentagonal faces at the midpoint of sides instead of at the dodecahedron vertices. Also a young relative in England made some intriguing related artwork!

On getting home to Melbourne, I started working on similar 1d to 3d constructions and plan to ferret around in the maths of the things soon. To make the 7 pointed star shown above, I needed to cut the craft sticks I had in 2 parts lengthways, soak the sticks, and also assemble them on a 3d printed jig.

Since then I have sourced some better craft sticks. On a trip to Northcote Plaza for a haircut, shopping, lunch and banking I also bought (hooray) some coffee stirrers which to me are just longer skinnier craft sticks. Their full name is "Premium Quality Eco Wooden Catering Coffee Stirrers" (!) Anyway with these it should be simple to make more models and more elaborate models. Hopefully by next week I can report on some 3d constructions,

Regards Steve Nurse  

 After a bit more work (ok its not work, just mucking around with the craft sticks) I have managed to make 2 of the platonic solids, the tetrahedron and the octahedron using 6 craft sticks per side. The inner circle of 6 stick crossings is glued to hold the shape together while the outer circle of crossings is left unglued: these crossings clamp onto cardboard which forms edges.

I've made a spreadsheet which works out the geometry of the faces based on the length of the  craft stick, the number of sides in the central polygon, and which stick ends coincides. From that spreadsheet its reasonably easy to draw and guess the feasability of various designs.  I'm not sure what I'll make next.

Update September 29

After giving one of my current lampshades to a friend I had a lampshade vacancy, so decided to make one from my current techniques with (mainly) craft sticks. Mk1 was a cube and I later expanded on it to make a 2 cube version. On mkII the translucent screen is baking paper. There are 10 sides in all on mkII, and I have left 6 of them open. The lamp is always against the wall, and the shadows of the craft sticks on the wall are a feature of the shade.  Craft sticks, baking paper, staples, glue, cut up manila folders.

 Continues here