triangle grid

1204: Basket Case

| wonko

Before Covid hit back in 2020, I had bought a slew of origami books, determined to work through them. One of them – “Origami Tessellations” by Eric Gjerde is one such volume that I barely scratched at the time. There is much richness to explore there, including this beauty:

This is “Basket Weave”, designed by Eric Gjerde. Folded from a 750x500mm rectangle of Kraft paper, on a fine triangle grid over the last few days.

The geometry here is mesmerising – the entire field used only 2 twists, alternating: Open Hexagon twists that rotate counter-clockwise and Closed Triangle twists rotating clockwise. The alternating rotations absorb the intersection conflicts but the folding is so dense (ie. these twists overlap) making the collapse an exercise in patience and perseverance indeed.

I struggled to find a regular rhythm when collapsing this tessellation – each molecule caused deep and awkward pleat overlaps and I could not devise wraps that would make them any less awkward. Working simultaneously on multiple molecules seemed easier as I did not bury so many axial creases while getting it to fold flat. The margins continued to be tangled.

I decided to pre-crease the open hexagons because I could derive the spacing accurately, reasoning that the triangle twists were the glue that set the hexagons in place – this I think saved me making some major blunders in collapsing, although I did notice a few times where the triangles twisted in the wrong direction making surrounding areas clash.

I am looking for a weave that I can fold VERY small, perhaps to make a lampshade of similar decorative inlay. I am not sure this is it as I am not sure i could physically fold this one much smaller without a lot more MUSH. This sheet ended up having pleats about 1cm wide – pleat width determines the size of the weave. My fat clumsy fingers would have struggled to navigate and collapse a smaller grid with this crease pattern.

Continue reading →

1187: Russian Lilac

| wonko

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.

Continue reading →

1082: Advent of Tessellations

| wonko

It was late in the semester, I was looking for a folding project (to add to the other 4 already on my board – procrastigami strikes again) and noticed in my feeds a 25-day program by Madonna Yoder called “Advent of Tess”. I guess I am supposed to know about Advent, having worked in a Catholic boys school for 33 years, but… apparently it is the 25 days in December leading up to Xmas (learn something every day)

The idea was that Madonna released a CP and a video tutorial each day for 25 days, victims start with hexagons of paper pre-creased into 16-grid triangles, and collapse increasingly difficult combinations of tessellation techniques on the page.

1-5 (front/back/backlit): Cluster 6, cluster 4, cluster 6 alternating, cluster 4 alternating, HT6 closed alternating

The first few were easy, and collapsed simply, but then I decided I did not need the tutorials and proceeded to mark up the paper with the day’s CP and collapse from that. This approach came awry pretty quickly as the elements began to argue for the same real estate on the sheet and I learned that sequential development was way more sustainable.

The folds started with closed triangle twists (something I had done a lot of previously, so found accurate placement of these fairly easy. We later progressed to “open” triangle twists, which are much harder, and require a “setup” that uses paper tension to define the lines off-grid that were the sides of the triangle.

6-10 (front/back/backlit): Triangle double-bar wells, shrinking violet, studded wheels, radiant, dancing ribbons

We then progressed to closed hexagon twists (again, something I had done lots of beforehand) and refined them into “open” hexagon twists – a fascinating variation of a “star puff” of which I had passing familiarity.

Continue reading →

942: Triangle Waterbomb Tessellation

| wonko

One of the interesting things about being associated with “Pinterest” is that their algorithms continually look for stuff it thinks will interest you. Given I only browse Origami, I get some interesting leads. I saw a triangle-based tessellation/corrugation and did a little digging:

triangle waterbomb tessellation

Seems Ron Resch, in the early 1970’s, was heavily into paper-based corrugation and this design emerged around then. The basis of this fold is 2 triangle grids, one at twice the scale of the other, offset at 30 degrees to the other. It took me a couple of failed attempts to get the crease layout to work but in retrospect is is much simpler than it seems.

Continue reading →

941: Home is where the Hive is…

| wonko

Over the last few years I have played with origami tessellations – the theory of a repeatable pattern that interacts with other repeats (molecules) is fascinating and a real testament to the accuracy of the pre-folding. As part of another project, I have been exploring triangle grids, and a devilishly tricky to collapse hex-cell tessellation by Robert Lang he calls “Honeycomb”.

Robert Lang’s Honeycomb Tessellation

After folding this a number of times, and then schematicizing the molecule, I noticed that “cells” were deep and, due to the nature of the collapsed layers inside I did not think they were very tidy nor kept their shape nicely. All to often, in origami design, paper thickness is disregarded in the theoretical collapse – in this case hiding away most of the paper in canyons between cells deforms them in ugly ways.

Original Lang molecule (right) and my shallow modified one (left) – same size paper

I started playing with the corner mechanism, and discovered I could halve the height of the cell wall, making the tuck much less bulky and doubling the size of the resultant folded field on the same bit of paper. Additionally it held itself together nicely with edges that are easy to stabilise. With a little practice (I am sure my work colleagues thought me obsessed, given the number of times I folded this tessellated field) I was ready to scale up … well, down in truth as I folded a “tiny” triangle grid on my target mustard leather-grain paper and then set the corner widgets before collapse only to then realise that folding this small was a real challenge with my nerve damaged, fat clumsy fingers.

CP of molecule (red=Mountain, blue=Valley) Thick lines are visible edges, thin are hidden
Continue reading →

545: Stacked Triangles Tessellation

| wonko

I spend a lot of time waiting for students to ask for assistance during practical assignment lessons. This  is a good thing – if they do not ask and are skilled enough to work independently then I have done the right thing, so it is all grist for the mill. (When kids need help but do nothing about it is much less good, but again a choice the student makes):545StackedTriangles

This is my first attempt (and probably last) at Eric Gjerde’s “Stacked Triangles” tessellation, based on a triangle grid that had a 6mm spacing. Continue reading →