geometry

Folding Algorithms – Sato Rose

| wonko

Much of Origami is algorithmic (algorithm = procedural solution to a problem). A rabbit ear is an algorithm, one knows how to fold it on a corner – double rabbit ear is the same solution, folded two simultaneously. Petal fold is also a standard maneuver which got me thinking of the Sato Rose algorithm.

I like this algorithm particularly because of the free-form nature of much of the folding, and the way it seems to “fit” a pentagon. I decided to use the same folding algorithm but try it with other regular polygons – I tried triangle(3), square(4), pentagon(5), hexagon(6), heptagon(7), octagon(8), nonagon(9) but gave up on the decagon(10).

The algorithm involves “nearly” bisecting each vertex to form an echo shape at the centre of the sheet – you then halve that internal echo to create a slightly offset echo and use that as the basis of a “kawasaki twist” Continue reading →

460: Torus

| wonko

Christmas is just around the corner, so I was thinking “wreath” shapes and stumbled across an astonishing torus made entirely of Tom Hull’s “Phizz” units:

The structure is based on twisted units that combine in 5’s (a pentagon has positive curvature), 6’s (a hexagon has zero curvature) and 7’s (a heptagon has negative curvature).

The inside has 10 heptagons and hexagon spacers, the outer rim has 10 pentagons with hexagon spacers and the rest of the shapes are hexagons.

This shape does my head in – heptagons take up more paper yet less space in the shape … huh? Negative curvature makes the inside of the donut by making a series of “saddles” which is pretty neat. Continue reading →

459: Electra

| wonko

Browsing an amazing book by David Mitchell called “Paper Crystals”, I spotted an interesting modular ball based on pentagons tiled with triangles named Electra.

Coupled with the original model was a suggestion that it was possible to make a 60 module version consisting of pentagons surrounded by squares separated by triangles. Continue reading →

Chiyogami/Washi Hex-Boxes

| wonko

When life gives you Chiyogami or hand-made Washi, with a relatively simple twist you can turn it into a hex-box: 

Lovely hand-printed Washi (swirls of fibres, block printed 20+ years ago) and modern Chiyogami (machine made but lovely) are actually fairly difficult to work with because you cannot see the creases and Fujimoto’s hex box establishes a bunch of landmarks to form the base-creases.

This is not a first fold, but the form and ingenious locking mechanism, slight variation to form lid and base make this one of my favourite folds – a jewel box when made from lovely paper.

Want one? Buy some nice paper (A3 or A4 work just fine, this is folded from a “golden rectangle”) and I will make it for you (or teach you how to make it yourself if you are near) – have your people call my people and we will make something beautiful together.

447: Black Forest Cuckoo Clock

| wonko

In need of some therapy, and with my procrastinator set on FULL, I embarked on a punishing box-pleating exercise:

I remember as a kid in New Zealand we had a cheezy Cuckoo Clock (Mum loved it) that used to have metal pinecones as counterweights and a faux timber case that used to “cuckoo” and scare the life out of me every hour. It had the loudest tick of any clock I remember.. I am fairly sure it did not survive the emmigration back to Oz because I do not remember it afterwards.

Robert Lang is known for beautiful mathematical models and when I first saw photos of his “Black Forest Cuckoo Clock” it seemed impossible to tease all that details out of an uncut sheet. Continue reading →

439: Nick Robinson’s Penrose Triangle

| wonko

The “Penrose Triangle”, also known as a Penrose Tribar is an impossible object:

If you look at any vertice it makes sense but the shape, as a whole, cannot exist … well, until now that is.

When I first saw folds of this I was intrigued, knowing a folder on Facebook, he suggested I approach the designer, Nick Robinson, who graciously shared his design with me (isn’t the interweb amazing). Continue reading →

433: Spikey Cuboctahedron

| wonko

So I have this line I sometimes use: “find some nice paper and I will make something for you”:

A friend (*waves to Jan*) found a packet of 15cm (ish) hand-printed Washi and teh challenge was on.

Continue reading →

431: Brill’s Woven Dodecahedron

| wonko

As a teacher, I look for activities, particularly in the establishment phase of a year, to engage. Nothing says engagement like a hands-on physical activity and, as my wont is origami, I went for a modular project:

The themes for this were many, the metaphors a plenty – “many hands make light work” and “the sum is greater that it’s parts” being central.

Continue reading →

420: Kamiya’s Diamond

| wonko

I have been exploring folded regular polyhedra, but came across this, a brilliant cut faceted diamond by Satoshi Kamiya and thought I would give it a go:

As a first fold, this is pretty sloppy to be honest – only after finishing it did the geometry I was laying down in pre-creases make sense. I have no doubt that when i re-fold this it will be much nicer.

This fold is a very clever bit of geometry, based on an octagonal piece of paper, making many facets and that classic jewellery diamond shape (this one would be a few hundret carats at that). The top face facets are locked in place by tiny closed sinks (making this very difficult I suspect to fold really small).

It is a pity there is no real locking mechanism to keep the model closed (I cheated and used a little sticky tape) – the bulk of paper does swirl in place but tends to spread when left – this might be different if made with a foil paper.

I seem to be folding a bunch of Kamiya models at the moment – prolly inspired by my latest Origami book purchase

417: Ornament

| wonko

I had a need, my brain was fried but I had to keep busy sooo…

I was given some lovely Yuzen squares (15cm) and, because the papers well all different, so colourful I decided to try to fold, from memory the Jackstone – unsure if my fat clumsy fingers could manage the fold so tiny.

I managed a dozen of them before the cramps and RSI flared up again. The resultant 6 pointed stars are so lovely, I threaded them on gold thread and gifted them to friends to put on their christmas tree (I do hope they like them).

When my hands settle down I might make some more – mind you it helps to have good paper.

411: Phizz-based Stellated Icosahedron

| wonko

The “phizz” unit designed by Tom Hull is a basic building block that can be used for many modulars:

I thought I would start manageable, so devised a 30 unit ball, 6 faces each of 5 colours – total of 30 units. These are easy folding and have a positive locking mechanism so were a good choice.

The tricksey part was to ensure an even colour balance – making sure that no face has the same colour twice. that did my head in a little, and it seemd to take me ages to come up with a construction method where I could easily predict what colour next to use.

In the end, a lovely modular – I may try for something grander, we shall see.

401: Double-Star Flexi-Cube

| wonko

It took me ages to even understand what this model was:

An ingenious design by David Brill, modular in construction composed of 3 different types of modules, clustered in threes, hinged together, it is a most perplexing construction.

A seemingly plain cube opens up to show a star, which fits wholly within the cube and is removable.

Flexing the cube makes another star, flexing the star makes a plank, stellated plain and other interesting twisted geometries.

This is a keeper – paper tension keeps it in shape generally but it does not strongly lock, so I may resort to cello-tape on the joints so it can be handled without risk of it disintegrating (as it did to me twice).

The geometry is interesting, photographing it seems not to do justice to the shapes but I am glad I finally nutted it out – bravo Mr Brill.

404: Joisel’s Bandonéon

| wonko

I first noticed this lovely little fold nestled amongst the masterpiece that is Eric Joisel’s Musicians, and decided that i must try to work out how to make it:

Now the “purists” amongst you will recognise this as a “Concertina”, but that is splitting hairs, given a “Bandonéon” is square, this is clearly hexagonal, but I digress.

Presenting a tantalising hand-drawn crease pattern idea on his memorial website, I decided to try and work out a method for this fold.

Unlike the original, my design is based on a 32 x 20 grid, making an extra gather in the bellows section (which is not a bad thing) and a simpler join along the long seam (which, sadly, I still needed to use double-sided tape to close).

The geometry of this model is really nice – the bellows almost fold themselves when the creases are laid in – I experimented with the seam in and thought it looked better with the strappy seams out in the bellows.

fashioning handles at the end happens quite naturally if you have been neat, and folding it without any extra creases is possible if you concentrate, making the presentation fold very tidy indeed.

I have folded many of these, they are lovely and, now I have a handle on the scaling factors and geometry there is a knack to making them that is quite easy to pick up.

On the same hand-drawn crease pattern, there is another that supposedly makes a saxophone – might give that a whirl as I seem to be in a musical instrument frame of mind at the moment. very happy with this one however, and need to move on from it.

400: Attack Of The Kraken

| wonko

There are many of what i would term “legendary” folds in the origami community – few more daunting that Brian Chan’s sculptural masterpiece “Attack Of The Kraken”:

I first saw pictures of this model when trolling around the internet looking for paper challenges: one piece of paper, you bend both a masted ship and a sea monster ripping it asunder – impossible surely. Amidst the turmoil there exists tiny details also – one tentacle contains a shard of ship rigging, another grasps the terrified yet defiant Captain – look closer, is that Captain Jack?

Annoyingly there seem to be no instructions on how to fold this thing – there was, however, a crease pattern adapted from a schematic Brian Chan tantalisingly left beside a display copy of his model so I started working on that. I photo-enlarged sections of the crease pattern and repeatedly folded them until I had discovered what to fold, in what order to make that section of the model work Continue reading →

399: Golden Snitch

| wonko

Exploring an Origami Tanteidan Convention book I came upon a model designed by Peter Farina I just had to try:

Being an out and proud Harry Potter fan, I know that the golden snitch is an essential component of any game of Quidditch, this one is a beauty.

Essentially using overlaying fan-pleats, you create the wings and enough paper to tease and shape round to make the body. Initially, my test fold was done in white paper and I found I had to be very careful (copy paper is so brittle) not to tear/split it – the middle section gets really damaged. Continue reading →