geometry

Bitter Sweet

| wonko

As I approached the date of my retirement, I genuinely struggled with how I could sum up my work-life, and how was going to say thankyou, personally, to so many people I have loved working with.

Collapsed blooms get shaped

It occurred to me that Origami could be my savior, and something hand-made and precious was the order of the day, so set about making Naomiki Sato’s pentagonal “Hybrid Tea” roses – in my opinion the zenith of his glorious rose designs. From a pentagon, with some skill, you sculpt a spiraling bloom of some 25 petals – genius as it is folds only – no cuts, no glue. Originally I was going to present them stemmed, but re-worked the idea to have them sit on calyxes instead.

I gave myself 3 weeks, and it turned out that was not really enough time, as each bloom from go to woe takes just over an hour – even when batch folding. It was a labour of love, and I got it done, and resulted in an amazing coincidence. I listed the recipients, and it totaled 33 – this number corresponded to the number of years I have been working at this current school – it was clearly meant to be.

Exacting pre-creasing

Acquiring paper, cutting perfect pentagons, calculating the relative size different between flower and calyx was the first task. I found if I cut the largest pentagon I could from an A3 sheet for the bloom, then the corresponding largest pentagon from an A4 sheet was perfect for the calyx.

Production-line techniques then ensued – precise pre-creases, pre-collapse wrangling and locating landmarks for secondary petal separation all have to be done first, and at this scale it is fiddly folding, and you need about 7 fingers on all of 3 of your hands. Once the dissected spiral collapse is complete the really hard part starts – shaping the petals to be soft curls in staggered cascades – quite a knack.

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Solving CPs

| wonko

Crease patterns, photo sequences and diagrams are the primary way of communicating the complexities and details of an origami model. While I am fairly capable of faithfully following even the most complicated diagram sequence, but still consider myself a newbie at solving CPs:

Origami-kimiro's CP

Sometimes the job is easier – lines are indicated as mountain/valley (red/blue or dashed/dot-dashed lines), other times you only get the major creases of the “base”, from which you then shape and tease the details from.

Origami-Kimiro, a Discord user on OrigamiDan released a CP for a simple domino toppling, and I knew I needed to give it a try:

my fold of Origami_kimiro's CP

Using 12″ duo Indigo Tuttle paper, I laid in the creases, oriented them in mountain/valley and marvelled as the paper collapsed into a base that was pretty close to done. Finishing the hand, colour changing to get the coat sleeve, posing and done.

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Showing Off 2022

| wonko

I was approached by the Holland Park Library again this year to mount an Origami display:

origami curated collection in progress

I decided to showcase based on 2 criteria: (1) Pushing the one square, no cuts to the limit; and (2) Using different shapes and modulars.

Collection location

Ferreting out archived models from various boxes, bags and cabinets, I put together a pleasing collection of origami models, designed by luminaries like Satoshi Kamiya, Robert Lang, Brian Chan, Eric Joisel and many others.

The collection gets locked up in glass cubes near the reading area of the main library, designed to be viewed from all angles, I am happy with the mix, location and visibility of this collection.

collection detail

I welcome you to come view, in the flesh, some astounding models.

1072: Fergus Currie’s Compound of 3 Cubes (Escher’s Solid)

| wonko

I sat in on a fold-along on Fakebook a few Sunday evenings ago where Fergus Currie demonstrted the folding of modules for this beauty – I got a little lost but on re-watch managed to nut out what was what:

Fergus Currie's Compound of 3 cubes (Escher's solid)

This is a compound of 3 cubes – each rotated on top of each other – when you see it you see it. It is comprised of 48 modules – 2 different shapes, 3 different colours (8 of each).

The folding is exacting, the angles and constructions accomplished and sophisticated, the tolerances for error are small. I think I was a victim of paper thickness when I folded mine – I used bond A3 photocopy paper because I had some lovely strong colours. The result of this choice was that layers get thick, some of the axes are not as crisp as I would like them to be, but it is finished, having taken a seeming age to fold and assemble.

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1071: 1st Stellation of the Rhombic dodecahedron (Escher’s Solid)

| wonko

I was invited to a “fold along” on Fakebook live by Fergus Currie, a multi-talented origamist with a penchant for geometric solids, I was free, and thought “why not”:

Ferdus Currie's 1st stellation of the Rhombic dodecahedron (Escher’s Solid)

Fergus demonstrated the folding sequences for 2 models taken from M.C. Escher’s “Waterfall” Lithograph, this one is the 1st stellation of the Rhombic dodecahedron (Escher’s Solid) – a remarkable 12-pointed solid with each unit being a slightly deformed pyramid.

unit folding

We started with unit folding, then moved on to construction techniques – a fun modular, in Fergus’ style of folding the entire vertex as a single unit, based on a template to geometrically construct the correct angles – neat stuff.

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1069: Starlight Kusudama

| wonko

Each year for the last 10 or so, as part of the “getting to know you” phase of a new year with my pastoral care group, we fold a kusudama together:

Starlight kusudama construction

The idea is simple, invite kids to sit, learn how to fold a module, then teach it to another mate … resulting in enough modules to assemble a megastructure.

Starlight Kusudama finished

This year I chose a 30 module designed by Vladimir Frolov, a Russian designer, a lovely starry ball.

The metaphor is really simple: “The WHOLE is greater than the SUM OF IT’S PARTS”

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1068: Russian Lilac Module

| wonko

I stumbled across the instructions for a glorious checkerboard kusudama designed by Andrey Ermakov, an insanely talented designer from Russia:

Russian Lilac unit designed by Andrey Ermakov
Russian Lilac unit

I decided to try and make ONE module – an exhausting process that starts with a HEXAGON initially divided into a 16 grid, then you dance through moves that flash and hide the reverse colour of the paper until you get this lovely pattern. This took me in excess of 2 hours!!! For ONE unit!!!!! You then crenelate and interweave them to make a spikey ball, tucking in tips to complete the tessellated surfaces.

Russian Lilac shaped to allow others to interlock.

Had I no life, and a LOT of paper, I would consider making all 30(!?!?!?!) of these things necessary to make the most complex spikey ball there is – a beauty that is not within my reach (for now) due to time pressures.

It is a timely reminder that astonishing and beautiful things come from Russia; ugly political and military action does not diminish this fact.

1067: Watermelon Colours

| wonko

So to avoid doing the growing list of things I should be doing, I decided on some procrastigami:

Xander Perrott's Laveau

One of the many “I must fold these” models from Xander Perrott’s forthcoming books, this is “Laveau”, a lovely 30 unit spikey flower ball that makes good use of duo paper.

Each unit, based on a 1:root(3) rectangle, folded from Tuttle Vibrant duo, I chose limey/crimson paper and began folding – I always love the almost meditative state you enter when unit folding on a production line – much the same as gridding before box pleating and tessellations.

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1066: Star Virus

| wonko

As part of the privilege of test-folding models for a forthcoming book, I also had access to brilliant new designs. I decided I must fold one of these for myself:

Xander Perrott's "Star Virus"

This is “Star Virus”, a relative of “Space Virus” that I had already folded (from his previous book) waaaaay back in 2020 at the beginning of the global pandemic.

The form of this kusudama is glorious – star-shaped protuberances from a glorious faceted sphere – reminiscent of the most popular visualisation of the Covid 19 virus, I decided to fold it in royal purple and yellow because Covid is mutating all the time, and this I see as a mutation of the original in every way.

Xander Perrott's "Star Virus" view

They say “if at first you don’t succeed, mutate and try again” seems to be the pandemic trajectory – this model has modules that are refined, positively lock and the whole spikey ball was such fun to fold.

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Test Folding

| wonko

Over the last couple of weeks I have been granted the privilege of test-folding the models from Xander Perrott’s new Kusudama book “Angular Elegance”:

Models 1-20 of 22 - 3-join
the 3-join of models 1-20

I bought Xander’s first book “Folded Forms” – a treasure trove of delicate spikey balls. I offered my services as a test folder – to my delight and amazement he said yes.

Test folding is different to model folding, the brief is to see how easy to follow the diagrams are, how reproducible the forms are and what sense the written instructions make.

As all the models in this book are unit-based, I folded 3 or 4 of the modules (rather than the entire 30+) to check the 2 types of joins and how regular the construction methods can become. There is a wonderful mix and variety of spikey balls in this new (as yet unpublished) collection, and the skill levels to complete them range from fairly easy to nearly impossible – which is good, challenges abound for all levels of folder competence.

Unit and join testing – 3+5joints (“Star Virus” kusudama)

Xander commonly uses some funky paper ratios in his base-papers. Commonly 1:root(3), but this collection uses 2:root(3) and more exotically 6:5root(3). The paper ratio allows construction of accurate angles (many based of multiples of 60 degrees), and the book demonstrates nicely how to cut sheets of this ratio from more conventional sized paper.

Each kusudama has it’s own quirks, tricks and stress points, all require accuracy and nice paper (most showcase duo coloured paper in flamboyant and wondrous ways).

I have not folded a book “cover to cover” since I was a kid (who only owned a only couple of origami books) – it was an intense but hopefully useful journey as I made notes about the instruction set, unit folding and assembly process, subsequently passing this on to Xander for his consideration.

As I approach retirement age, I can see myself doing more in the meta origami world, having already established myself as an origami book editor and test folder – having time to do this without having to shoe-horn it inbetween school commitments is a luxury I am looking forward to.

1064: Fergus Currie’s “Frustum”

| wonko

An invitation went out on Fakebook to join a “fold along” session with Fergus Currie and, although it was after 11pm local time I thought why not:

Fergus Currie's "Frustum"

Fergus taught the module then construction of a 4-part modular Frustum (a truncated pyramid) – an ingenius and “frustrating” model in that the lock between modules is accomplished using a “latch crimp” tab inside the bent gusset pocket, making the actual construction a little fiddly.

I found I needed to ease the 3rd and 4th modules in place using long-nosed tweezers, when it sits right it locks tight but requires a bit of a controlled jiggle to get it to be seated just right. The final module is a bit of a challenge to insert without dislocating the two either side of it.

Patience and tweezers finally won over and the top half finally was locked tight and tidy, then a simple weave on the bottom flaps complete a lovely truncated pyramid. Material thickness is an issue here – the tab-pocket system assumes material of negligible thickness. If you use heavier paper you need to fractionally adjust either the pocket depth or the tab length – fortunately there are a couple of fold junctures that make this easier.

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1062: Omicron

| wonko

Having recently purchased a bumper pack of 6″ duo paper, I was itching to fold something with it. Given we are in a new wave of Covid-19 (Omicron), I thought a virus-like kusudama was in order:

Xander Perrott's "Minaret"

This is Xander Perrott’s lovely modular design “Minaret”, a 30-piece ball of wonder.

Each piece is based on a 1: root(3) proportioned rectangles, intricately collapsed into beams with tabs/pockets on each end.

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1060: Second Stellation of a Cuboctrahedron

| wonko

To celebrate the release of his lovely new book of modular polyhedra (must get me one), Fergus Currie offered an early morning (for me at least on the opposite side of the planet) workshop on how to fold his second stellation of a cuboctahedron:

The second stellation of a cuboctahedron

I set an alarm, awoke at 1am and folded along with Fergus.

I like this modular a LOT – each vertex is a single piece of paper – it works well with paper that has only one side printed or printer paper. The design is ingenius, the angles odd and exacting but you get into a groove and they make sense in the end.

The second stellation of a cuboctahedron VIEWS

I went into production line, and using the template to establish the initial odd division, I found that using a fine ball stylus and ruler it was easier to lay in the intermediate creases with the accuracy to make the vertices crisp and accurate.

Once I had 24 units, I then interlocked them in groups of 3 using the narrow tabs and pockets – these interlock really tightly and I could not imagine trying to do these later. I then joined the triples as they tile on longer tab-pocket sets that slide together with a little encouragement. Eventually the units combine to become this wonderful spikey ball with unique geometry.

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1058: Twister A

| wonko

Clocking on for another round of procrastigami, I decided to give the first of the “twister” series a go:

Twister A by Ilan Garibi - 2x2 molecules
Twister A – 2×2 molecules

This is “Twister A”, designed by Ilan Garibi, a lovely dimensional fold with a final twist to finish it off.

I have folded a few square twists, this one perches a twist on top of the intersection of opposing ridges, contains remarkably few folds on top of the base square grid.

Twister A by Ilan Garibi - molecule
Twister A Single Molecule

The basic molecule tiles awkwardly – because of the directionality (it forms in a clockwise direction) of the molecule, you have to reverse adjacent molecules if you want them to line up.

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1057: In ‘da ‘Hood

| wonko

Exploring Ilan Garibi’s lovely book “Origami Tessellations for Everybody”, the next “family” of folds starts off with “Childhood” and then evolves into more of the same:

childhood evolved
Childhood-Evolved (4×4 molecules)

This is almost a corrugation, as there are nearly no layers overlaying others – the surface treatment is deliciously dimensional, and the distortions are caused by paper tension and torsion of the underlying square-twists.

Childhood Molecule
“Childhood” molecule

I started with standard cotton-based photocopy paper (which for me is a LOT like thin Elephant Hide) and laid in a square grid. Both childhood and childhood-evolved use off divisions. I folded a regular division (halves or thirds), then halved until I was close to the required grid sizes, then sliced off unneeded units before laying in the wedge-shaped mountain creases.

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