1204: Basket Case

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.

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546: Château Chinon Tessellation

Another time sponge, based on a square grid initially that was torturous to fold and pre-crease. Based on Eric Gjerde’s tessellation molecule, it is an amazing use of paper that features largely an “all at once” collapse.546ChateauChinon

Many tessellations sit flat while you do them, their interim stages are still flat – not this mongrel. Once you start, you gotta finish and then work out how to flatten – interesting but not very portable in the end. Continue reading

545: Stacked Triangles Tessellation

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

534: Friday

Continuing my exploration of some of Eric Gjerde’s introductory tessellations, I liked the look of a square-twist based weave:534Weave

Sitting on a square grid, off-set squares are added to near diagonals and twist to collapse and lay flat again. The front side then is a jumble of rolling squares but when you flip it over to the waste side a lovely weave pattern has been made as a side effect of the surface twisting. Continue reading

533: Gjerde’s Pinwheel Tessellation

After leafing through Eric Gjerde’s “Origami Tessellations” I knew I had found the motherload of paper punishment:Tessellation6

This is the “Pinwheel” tessellation and it has a hidden beauty. I am learning that a tessellation is a regular repeating pattern, magically interlocking “molecules” that go together like tiles on a mosaic floor.

Usually based on a grid (at least initially), this one is based on a triangle grid, and features closed hexagon twists and open triangle twists that compliment each others vertices very neatly. Backlit they reveal an intense and curious but often completely different geometry. Continue reading