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

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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1064: Fergus Currie’s “Frustum”

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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1060: Second Stellation of a Cuboctrahedron

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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1051: Rhombic Triacontahedron

Origami designer Fergus Curry shared with me the diagrams for his Rhombic Triacontahedon, I was determined to give it a try:

Rhombic Triacontahedron

30 squares in 5 colours, some clever unit folding later and I had the bits needed to construct this little gem. A positive tab-pocket mechanism, some strategic placement of colours and pretty soon you have a lovely sphere made of rhombi. [edit]: A friend (JZag) pointed out this is a D30 (DnD reference there) – nice and nerdy.

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