WIP – a duo of interlinked Torusses

For Xmas, my son Matt gave me a day a page Gary Larson desk calendar. Knowing me, I noticed the tear-off pages were square so, in a moment of madness I decided to fold something with ALL of it:

Exploring scale (and remembering the disaster in finished size that was my last attempt at a torus), I decided a PHIZZ based structure would be fun, with a torus being suitably visually interesting so set about folding units for them from the quartered pages. After 3 months I had enough (360+) to connect up the first torus, then began accumulating units for the planned second.

A longitudinal fold like this requires patience and persistence – making any part of the structure required LOTS of units, so you just gotta wait for the days to go by,

During July, I had enough units to complete the second Torus, deciding they needed to be interlinked, and began to work out HOW to connect up the units while being connected to another torus. Logistically this ramps up the difficulty exponentially – coupled with the fact that I initially connected the loop INSIDE OUT, requiring me to unpick it and invert it before re-joining it.

I am not sure if the inside diameter of the donut hole is wide enough to have 2 torusses passing through it – I _think_ it will be ok with a small amount of squishing, but I guess we will find out in 3 months.

The resultant dual torus chain is visually awesome, the geometry of 5,6 and 7-sided polygon meshes that comprise the curves are really interesting to look at, and it sort of self-supports, making display fun.

Folding over such an elongated period of time is exhausting. Keeping the model save and clean for that time so it all looks like it was made together is also a challenge I am currently working through.

Half way through the journey and i am still keen … we shall see how long that lasts.

1205: Blooming Bow

Having international connections with folders continues to be a gift. Connecting via my Instagram account, I was approached by a new Kusudama designer Syed Faraz approached me regarding his new design “Blooming Bow”:

He asked if I could diagram it for him. I insisted on folding it first.

In folding it, I got a better appreciation for the steps (from a rough photo diagram sequence), and helped me refine the shape of the unit, capturing more accurately the sequence.

This kusudama is of the “curler” variety – it differs from others in that rather than a tab-pocket unit connection it relies on the interlinking of paper curls.

I have folded a couple of “curlers” and note that construction is generally more difficult – the units tenuously interlock until you “triangulate” and they stabilise. Getting the curl right is really important – the centre of the kusudama gets very dense as you add more 5-3 groups.

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1197: Java Sparrow

The Java Sparrow is a type of Finch, and is characterised by some very brightly coloured but well confined patches of colour. It represents a challenge for an origami purist because it typically needs 4 colours, and paper is usually (at most) duo colour:

The approach of this model, like a few in Kyohei Katsuta’s repertoire, is to use multiple (in this case 2) sheets of paper folded in together to give you access to the double colour pallet.

You know that feeling you have seen something before – I get it in origami a lot. I was sure I had seen a “Java Sparrow” before, and was sure it was in a Robert Harbin book from my youth, turns out the one I actually remembered was in an equally old book I had as a kid (and still own) “Origami” by Toyoaki Kawai which I remember clearly used a colour change “cheat” that involved colouring in parts of the square strategically with colours that would be presentation areas in the final fold. This “technique” is currently called “Kimiroing” because a modern designer (Kimiro) uses little laminated (or sometimes painted) colour patches to achieve tightly controlled colour change in some of his models sometimes.

I searched my stash for suitable paper and settled on blue/black thick Shadow Thai, and orange/white Yukogami, cut 25cm squares of each and then set about nursing the thick papers through a lovely but precise sequence.

Although uniaxial (bi-symmetrical along a long axis), the shaping ensures the model does not spread open like so many in that ilk. The legs are really fine – a little too thin to support the model weight, but I will probably mount it on a wire armature to fix that. The sequence lets you use quite thick paper while still managing the layer build-up well. Even though I struggled to get a square of Yukogami that was actually square because of the rough texture, the results of the mixed paper types give the model the illusion of a fluffy tummy, scaly feet and smooth flight feathers.

I really love the result, and think it a good display model for my next cabinet exhibition.

1194: 3 Gyroelongated Square Dipyramids

Just trying to get my head and mouth around the name of this geometric modular provided the imperative to fold it:

Designed by Daniel Kwan, it is based around Francis Ow’s 60 degree unit, folded on a 4:1 rectangle that then has 30 degree crimps placed at thirds down the length of the paper, on opposite ends. The resulting units seem to spiral.

Units are joined in groups of 4, making a single solid descriptively called a “Gyroelongated square dipyramid” – “gyroelongated” meaning it is an extruded and twisted solid, “Dipyramid” because there is a regular square-based pyramid at each end of the solid.

Daniel illustrated they could be interwoven – 3 can be symmetrically interwined to make a visually startling whole.

The hardest part of this model was working out the symmetry of the intertwining. Merely seeing a finished one was not enough, you need to discover the scheme that, symmetrically, distributes spokes of each sold over and under, taking into account the twist, yet still meet at a pyramidal end WITHOUT overly distorting the units.

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Hana Midoh (Sweet Shower House for Celebration Buddha Just Born)

Ages ago, using up the white papers from a cheapo pack of coloured 15cm square origami papers, I first had a go at folding an origami “Spirit House”:

Designed by Ichiro Kinoshita, this model emerged from my “to fold” pile and it was meant to be.

I had not long returned from a trip to Japan (in the late nineties), and fell in love with the idea of having a Spirit House at our front door. Apparently it is a tradition to provide a home for good spirits – they then repel bad spirits. We have had our “spirit house” for decades, I love it.

I decided it was time to fold a better version of the rough first go, so turned to my stash of hand-made Kozo and cotton paper I had made from pulp back in October 2024 – it has a “stone-like” appearance so I thought it would be perfect.

I cut 3 18x18cm squares and a 20cm square, then set about folding the parts (it is sort of a modular, 2 parts of which need to be glued together). The paper is fairly thick and fabric-like, but takes folds fairly well. I used some strategic glue spots to keep seams closed, wrestled a little with the thickness but was happy with the results in the end.

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1187: Russian Lilac

30 unit modulars exist in many forms, permutations and complications, few rival “Russian Lilac” for sheer time-consuming brutality:

Designed by Andrey Ermakov, this astonishing spikey ball has been quite a journey. I first added it to my “to fold” pile for a few years now, and then narrowly missed folding it as part of the IOIO (Internet Origami Olympiad) in 2021 – it was the nightmare round 2 task (I was knocked out in round 1).

The FIRST hurdle for folding this is the need to create 30 perfect regular hexagons that are all the same size (I created a few extra just in case shit went sideways). To do this, I cleaved a 2.1:1 rectangle from a 70cm wide roll of white/natural Kraft paper. Using 47 construction lines to form a regular TRIANGLE GRID on this page, I was then able to isolate 35 adjacent hexagons, which I then cut out carefully (scissors warning!!!).

Each hexagon then receives a 16 grid in all 3 axes, then 4 extra pre-creases before you begin unit folding. This totaled 1470 pre-creasing. Having bailed near the end of this year’s “Advent of Tessellations”, determined to return to it after some distance, I am not sure why i then bounced to another triangle grid on hexagon marathon project – I am guessing the time with my counsellor will eventually surface the reasons for the self-inflicted PTSD 😛

To form each unit, each hexagon then goes through 79 processes – all up each unit took me just over an hour each.

The main premise behind “2d colour-change origami” models (of which the flattened unit is one) is that you strategically utilise the edges of the sheet so you can reveal both sides of the paper along it by some clever flanges and flipping. The GENIUS of this model is that we use colour change to (when assembled) establish a colour-change triangle checkerboard across ALL outer faces of the finished polygon. Sadly each little triangle is not SEAMLESS – most are but not all, but based on my experience folding Daniel Brown’s seamless chessboards, I know this provision makes the design infinitely harder.

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1176: Taj Mahal

Grinding through my “must fold” pile, I decided to work on the modular “Taj Mahal” designed by Valentina Minayeva:

I am a member of PAQ (Papermakers and Artists QLD) and this month’s meeting was all about “working with colour” – as I am not really into painting, stitching and similar, the closest I get to colourful “collage” is multi-colour kusudamas, and this is a beauty.

A relatively simple bi-colour unit combines with adjacent units to make some fascinating emergent geometry – we see colour wheel points, and tri-colour cubes emerge from the tangle in fascinating and delicious ways.

Unlike many kusudamas, this one has a relatively simple unit locking mechanism – the tabs positively lock into the pockets – the REAL challenge is colour distribution.

I decided on 5 colours (because it is a 5’s and 3’s type construction (5 units connect to make a swirl of a point, and adjacent modules dock in 3s). So I needed 6 sheets of each of the 5 colours to make a total of 30 units. The first swirl dictated EVERY other placement, as the next unit to add is the colour of the one on the opposite side of the structure. Once I saw that, it was a bit of a 3d jigsaw puzzle from hell, but satisfying.

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1169: Xander Perrott’s “Conglomerate”

Multi-unit Kusudama folding is something I enjoy – the emergent geometry and intricate interlocking of units to make a whole is very satisfying. None more than “Conglomerate” designed by Xander Perrott:

When I saw his fold on insta I knew I wanted to fold it – I had not seen anything quite like it, so I reached out to Xander and he shared instructions – how wonderful is the internet?

Let’s break this down – the kusudama is composed of 30 units, each folded from a rectangle in the proportions of 1: sqrt(3). Each unit has a triangle grid imposed on it, with triangular gussets to allow the “facets” of the faces to become 3D.

The geometry of the unit is very pleasing to fold, it all feels really natural, and the tiny collapse of the unit to make it 3D also feels right.

Interlocking the units …. now that seems to have taken me an age – each unit cups around one lobe and inside another lobe, forming a many-layered, staggered icosahedrons – each locked into place at multiple anchor points. It took me a while to master the locking process, then re-learn it as the orientation turned this way and that, but this kusudama needs no glue, and when a unit is fully locked in it is really rigid and strong.

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1150: Star Katrina

As a closet botanist, I am interested in floral geometry – many flowers are based on pentagons:

This is “Star Katrina”, a beautiful kusudama designed by Xander Perrott. Folded from 30 x 2:root 3 rectangles cleaved from squares of Tuttle Indigo dye duo paper over the last couple of days.

The unit is based on a tight triangle grid – fairly easy to fold accurately and the locking mechanism is so positive that this kusudama is held together via paper tension and friction only (no glue, truly, none).

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Display

My annual origami display at Holland Park Library was installed this morning:

Cabinet 1 views

Included is a broad range of origami styles from a huge and diverse collection of designers, folded from a varied collection of papers.

Cabinet 2 views

I am trying to get better at not crowding the display cabinets – sometimes less is more to allow individual models to shine – let me know how I went.

If you visited, I would love your impressions, comments and suggestions for future displays.

Get directions here

1114: Fergus Currie’s 3rd Stellation of an Icosahedron

Just before the Origami Marathon this year, Fergus Curry dropped a free access download to a new hedron that I knew I had to try. I cut the 30 papers and then ran out of time to actually fold them prior to the marathon:

Returning to this fold recently, I went into production-line mode to ensure I had fold consistency for each module given angle construction was a core requirement (ie. there is no “template”, you make the angles fresh each page, twice).

The resultant module have a pair of hinged triangles as faces, and deep pockets and twice bent tabs that, when together, make a really positive join.

Construction was at times painful – seating the modules inside their nearest neighbors requires you insert a tab around a corner that is being pulled closed as you seat it. Early on, mating modules is ok but as you lose access to the inside of the solid, it becomes more and more awkward. I resorted to a symphony of tweezers near the end to close it up.

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1112: Binding Cube

One of many things I like about being a subscriber of JOAS’ Tanteidan Magazine, is the little modulars that usually start each edition. Leafing through #191, I spotted a series of cubes designed by Jun Maekawa:

My pick of the cubes is his “Binding Cube”, a delicious little 6-piece modular whose layers lock so completely and tidily, the cube looks like it is one piece.

Folded from 3 squares of Tuttle duo each split into 2:1 rectangles. The module is relatively simply folded from thirds, the lock has layers of adjacent modules interleaving in such a clever way. Some of the modules were hard to place because the lock has very little clearance if folded accurately.

I like this model a lot, and am also happy with the colour choice.

1108: Poco Poco

Browsing the current Tanteidan magazine, as you do (if you are a paid up member of JOAS), I saw a curious design for a “yummy” rounded unit, designed by Miyuki Kawamura, and decided to fold one:

The fold sequence is simple, the collapse creates a volumetric, rounded, colour-changed “eye-ball” like unit that holds itself together using paper tension. Like most unit designs, it has flaps and pockets, so I had to fold another 2 to see how they connect.

Again, by the miracle of paper tension 3 units unite into a lovely cube corner, so I had to fold another 3 units to make the smallest solid kusudama, again positively locked and, boy, the geometry is fascinating.

Nestled in among the eyeballs is a perfect cube. I may fold more of these (however I will fold using a smaller paper (I used 15cm square, but can easily fold smaller) as I think the 30 module is the pinnacle of weird but interesting kusudama.

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1096: WXYZ

I was approached by the publishers of the book “MODULAR ORIGAMI – 18 Colorful and Customizable Folded Paper Sculptures” by Tung Ken Lam, and asked for my impressions:

I received it just before going on an overseas holiday, so have only just begun exploring this soft cover edition.

I decided to start with some pure geometry – the result of 4 planes intersection each other – a wxyz.

The instructions are well laid out and easy to follow, I chose 12 sheets of paper, 4 colours, 3 of each. The module reminds me of the XYZ that I have folded previously, but the cunning use of 60/30 degrees in the construction lets all 4 planes nestle accurately together in a rather pleasing way.

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Day Tripping to Zaragoza

So a fairly well known fact in Origami circles is that there are Origami Museums, few compare in size to the Spanish one in Zaragoza.  When Jo and I had decided to spend time in Barcelona, we discovered Zaragoza was doable day trip from Barcelona Sants regional train station, so a plan was hatched.

Barcelona Sants is a regional rail hub, different to the metro. We will from depart here in a few days for Province, but this station also provides access to many other places in Catalunya and beyond. After locating our platform ( via a very helpful man at the Information counter), we had our bags (and everything else) xrayed before arriving on the platform to find the train already boarding.

We boarded AVE-S112 High Speed train, allocated seats a lot like an airplane, and took off. The train sped underground until it cleared the central city and burst out into the light as farmland flew by. For a lot of the journey the train was topping 295 km/h as it hurtled stop to stop.

After a little over an hour, we arrived at Zaragoza train station, and de-trained, got some refreshments then headed over to the Bus Station, to catch a C1 circle line bus, and rode it the remaining half way around to the terminus. After a brief bit of nav we were picking through the back streets to EMOZ, located on the 2nd Floor of Centro de Historias, Plaza San Agustín 2.

I had been in contact with the museum ever since there seemed a chance for me to visit, and it was lovely to finally meet an online friend named Jesús Artigas. We nerded out a bit, talked about the current exhibition and about Yoshizawa’s works, and particularly the work of Eric Joisel. 

The museum has, on display a number of Joisel’s original works, including one of his gnome orchestras, his large-scale Rhinoceros and his large scale Pegasus.

Jesús let us sneak peak in the store room at Joisel’s large Hippopotamus also, all master works from a genius artist much missed. 

We talked folding, design, and it turns out he is working on an interesting origami publication of endangered Spanish animals, and asked if I was interested in test folding closer to publication date. What an honor indeed, naturally I said yes. That should be fabulous and something else to be involved in when I finally return home.

We parted company with the promise of future collaboration, then Jo and I took our time appreciating the many rooms of exhibits. It was good to see so many original works from legends in the field, including Victor Coeurjoly, Robert Lang, Junior Fritz Jaquett, Kashiwamura, Jozsef Zsebe, a host of different Vietnamese designers, and even a tiny work from Yoshizawa himself. We are not worthy.

The museum also offers informative information about the paper/folding traditions of many countries. It is interesting that many different schools of folding crafts emerged independently with the introduction of paper and paper-like materials. We also saw some very early traditional folds pioneering skills from historical giants that modern day origami designers stand on the shoulders of.

The feature artist at the moment is Vivian Berty, with a number of rooms devoted to her colourful, figurative and representational varied art practice. Such a riot of colour and range of simple to elegant models, compositions and modular works.

It felt like home for me, to be surrounded by an art form I have spent a lot of my life exploring. Nerd-feasts come in every flavour, and this was one of mine. 

After leaving EMOZ, we reversed our journey to Zaragoza Delicias rail station, grabbed a late lunch and then our train back to Barcelona. I am sure I gushed, Jo was very tolerant of a very happy nerd. If I get the opportunity I would like to visit again, as well as explore the other origami museums of the world.