An orderly tangle

A paper version, I haven't made this yet, just cut the pieces.

Hi

After a few weeks of trying, I have managed to make my first "orderly tangle" or "regular polylink" which is a type of link (lots of loops tangled up) made by rotating and interlinking regular polygon shaped loops on the face of a solid. These shapes are described in a book by Alan Holden called (unsurprisingly) Orderly Tangles.  I have written and submitted an article on twin edge polyhedral links and knots (see my last post ) , and during the review process, Holden's work was recommended to me. After resubmitting the article and also seeing online examples, I decided to have a go myself. There are articles by George Hart describing paper and other tangles here and here , but the one I made was based on Alan Holden's work. From here I might be able to work out the maths of the things and could go on to make them from other materials (beer cans being seem to me the most obvious).

Anyway my steps were - 

* Get a copy of Orderly Tangles, I needed to do this for my article anyway.

* Work out what I wanted to make. (This was an easy choice, I had made topologically similar cubes before)  

* Look up the dimensions needed and stick to the proportions - I used 1/4" = 10mm as a scale.

* Replicate the squares Holden used in a 2-part 3d print - 2 identical C shapes plug into each other.

* Attempt assembly without jig (really hard, I mucked around and made "other stuff" with the 12 pieces instead.

* Go back to the original photo and work out the proportions of a jig - it could be based on a 16mm square rod about 100mm long.

* Design and print a cross-shaped jig that could come apart from inside the polylink

*  Strap 2 squares to the jig with rubber bands, and keep putting more squares on as per the photo. To assemble the last square in I had to crop the pin on each side by about 5mm, the fit was too tight otherwise.

* Disassemble the jig et voila!

Regards Steve Nurse

For 3d print files see https://www.thingiverse.com/thing:7366096  

 

 

 

 

Topology Lecture at Monash

 

With Dan at lunch, I'm in blue

Took some unsuccessful steps to not get lost, I had this as a phone photo.

Huntingdale Station

The new routes explained

The blurb and 

several part-pages from the presentation,

Hi

 After more than a year of work and discussions with the publishers, I am hoping some of my maths work will be officially released soon. I haven't waited around though and when reviewers asked "has the work been used in education?", I had to say no, but then went on to ask my University maths contacts if I could present the work. After a few days, Daniel Mathews of Monash came through and invited me to speak to Monash postgrad topology students and researchers. I was most honoured, said yes, and got working on my presentation about a week before the due day.

It all came together quite well. By the night before the presentation, the work was finished and I'd rehearsed and even timed it. On the day itself, I headed off by bike, through some rain, but with a rain jacket on so no real stress. There were new (to me) arrangements for Dandenong line trains which I had to negotiate but that wasn't too hard either. Unfortunately I got off at the wrong station (Clayton not Huntingdale) and spent a bit of a confusing time getting a bit lost before finally reaching the maths building. I remembered it even after 10 or so years, had a rest, a bread roll and some water in the lobby, then went up to meet Dan.

The lecture went well. Having mild stress (rain, train changes, getting a bit lost) before the lecture didn't hurt and I got through it all quite well. The only questions were about "chamfering", which most of the students hadn't heard of. After the lecture I was shouted lunch by the maths department which went well, and then one of the students and I had a maths chat. After that it was back on the bike and home. This time I managed to get straight to Huntingdale and was whisked home pretty quickly and without suffering under deluges.

This link takes you to the Thingiverse page where last week's talk, a preprint of the full article and parts for constructions (as 3d printable stl files) are all available. I welcome any correspondence and questions!

 Regards Steve Nurse 

Small Monolithic Statue

 

Detail and obverse

Bike seat frame being varnished

The round bits came from here.

Used some bolts and Nyloc nuts from the Eames chair to fix the seat on this bike.

Things are a bit unstable in the world right now we have a former ally with a president who is running rampant seeking regime change in countries other than his own which is a bit upsetting. Now it's not only news that is filtering in from around the world. It is affecting most Australians materially, with petrol prices rising and fuel supplies generally less certain. In the context of all these regime changes, images of toppling sculptures of world leaders have been running through my head. My junk sculpture practice has sort of drifted towards making my own grand - mock world leader sculpture. Yes it is only about 60 centimetres high however placed in the right spot and with a bit of squinting it possibly looks bigger.

The main bits of these sculpture are at the top and they are adapters for fitting disc brakes on bicycles. I ordered them from eBay and they look quite good but I'm not quite ready to try them out yet. They are held together by a used-up lip balm dispenser. The shaft of the plane is from a dead Eames inspired chair found on a junk heap. In the last few days I have harvested bolts and nuts from this chair to fix a bicycle. The base is made from a box of leftover routed timber bicycle frame components which I have been rummaging through and rescuing. Finally I was varnishing and repairing timber bicycle seats and using builders bog and varnish - with these I finished off the plinth.

So there's a lot going on in the world - not all of it nice and sometimes not a lot we can do about it. But at least in Australia we can reduce dependency on foreign energy - maybe ride a bike a bit more, maybe put up a solar panel or two, and maybe support more onshore processing and use of Australian crude oil and gas. But in the short term and as an immediate reaction there is always art.

CD Clock on Thingiverse

 

Today I put a clock design up on thingiverse, here is the link, https://www.thingiverse.com/thing:7316196 . 

 This is an old design for me and up till now I have resisted making it public. It needs a cd, a rubber band and a clock mechanism to work. Its standard position is hanging on a wall, but it also has 3 holes for 3mm legs to make it a desk or table clock - just add skewers!

 The 2 centre parts of the design are dependent on the clock mechanism you are using, but the numbers should all attach radially to any DVD or CD using a rubber band as a fastener. The design is a version of a previous design, the printer spool clock, also on thingiverse at https://www.thingiverse.com/thing:2531561 . As well as a clock, this design could be used as a counting toy, and a way of learning about factors. Have fun! 

As well as plain clocks, I have experimented with variations, most notably face rotation clocks (the hour hand is anchored and the whole face rotates) and tetrahedral - cd - clocks. Some related posts are 

here, here and here 

 Regards Steve Nurse 

Photoframe, Strainer and Stopper on Thingiverse

 

Hi

Today I've added 3 new things to my thingiverse web pages, and these are a diy photo frame, a bowl strainer and a stopper for a Black and Decker Workmate sawhorse. The stopper is probably the least creative doo-dah in this lot but it is what made me get off my bum and put all the designs on thingiverse. I went to my friend Christine's for dinner, and she commissioned the stoppers to tidy up her sawhorse. Before I'd even designed the stopper (she gave me an original one) I realised that the sawhorse at Wecycle needed repairing too. Within a week or so from the commission, sawhorses at Wecycle and Christine's were fixed. My friend Myy said he'd like access to 3d printed things at his repair cafe, and so I've made it available.

The photo frame design I've had and used for a while, and quite like it.

The strainer is quite new - I gave one to Christine although she didn't have a bowl which suited it properly. Maybe it could be useful for her as a cat frisbee?

(Links above are to thingiverse pages which allow a 3d-printable STL file to be downloaded) 

Regards

Steve Nurse 

 

 

 

Bridges 2026 preview

 

These are the steps to making a compact dodecahedron (see the compact octahedron shown here) from faces made from 5 coffee stirrers. This is new work and the start is to make the reciprocating frame sides using the black jig and a cad image showing the right placement of sticks relative to the jig. An stl for the jig is here.

 

All the sides, and 

The sides made into a dodecaheron with a spare side

 

The dodecahedron

There are 2 types of dodecahedron available from these sides. I've made the version shown in purple above, which has the edge joins near the corners. As shown below in "net" and "link" versions, the links created are different.

Hi

Last year I attended a maths and arts conference called Bridges. I'm a retired engineer and dabbling in the maths and arts fields is fun, interesting and challenging for me. It's lucky that I've been an engineer and now live in a time where there are affordable computers, 3D CAD packages and 3D printers. This means I can use and access some powerful artistic tools. 

At the end of last year, the chance came up to present at a local maths conference - it had a Maths and Arts lecture stream and a Maths and Art exhibition and I came up with some new work for that. It's not officially published as there are no conference proceedings, and there was no requirement to submit a paper in conjunction with the conference. That was good as it was easy to get a foot in the door and make the presentation, but not good as no legitimate publication resulted. I've unofficially published anyway, just parking the presentations along with the 3D printed parts required to replicate my work which on thingiverse here and here. 

Now all the rush to produce the work for the conference is over and so is a summer holiday season. Hopefully also the horrible hot summer weather and bushfires are over also! Anyway, its February now and I've sort of been spat out into the new year and need to work out what I want to do with it. The chance to present at and attend Bridges 2026 is there, and having presented at the local maths conference there's some material I can write up. But but when I looked at the deadline for papers it was an oh sh!* moment. The deadline for standard 8 page papers is already past, and if I want to write a short paper or run a workshop then I need to write and submit in February. 

Meanwhile, after not thinking about maths stuff for a bit over a month, I have returned to it now and am starting to see the work I did in late 2025 from a different perspective and am making and calculating new arrangements of parts from the jigs I made last year. An example is shown above.

There are some nice templates for short papers on the work already done. I had heard of Doris Schatschneider before Bridges last year and met her briefly at the conference. She has written a nice paper on some of M.C. Escher's commercial artwork and its in the monumentous and free Bridges archive here. Four Pages doesn't sound like much but they are four squishy pages which use a small font (1800 words or so) and still manage to fit in some nice illustrations. For the workshop papers somebody I know from Melbourne is the chair of the sessions, and I attended 2 workhop sessions last year. It cannot be that hard!

So the plan for now is to write a 4 pager and have it ready to go, and then work on a workshop session and paper. If I'm not happy with the workshop paper I will be able to fall back on the 4 pager.

Wish me luck! 

Update, Feb 9, 2026

While watching Dog Park on ABC iview,  I finished the second dodecahedron version I'd mentioned and sketched above. pics are below. 

The 2 types of dodecahedron which can be made from the same side.

Several 5 stick bands can be seen in these structures which are topological links. On one, the bands are outside the pentagon shape and an the other they are inside.

New Dodecahedron with side

New dodecahedron