Origami Trapdoor Spider

Trapdoor spiders are big spiders living in burrow, hiding behind door they constructed out of available material. Any unfortunate critter wandering too close will be ambushed and eaten.

I made a specific kind, called ravine trapdoor spider (Cyclocosmia truncata) whose rear end of their abdomen is flat, hardened, and has interesting pattern. Like many big spiders, they are vulnerable to parasitic wasps. Upon burrow invasion, they will position themselves within the burrow so that their hardened end faces the invader. Apparently it's tough enough to protect against sting.

Design

Back in November 2024, Origami Dan had a design contest whose theme was "in the style of another artist". I had some ideas but no inspiration to design. Just 3 days before the end of the month, another idea came to make this trapdoor spider. Like me, you might recognize it from images circulating online.

The spider will be made in Kota Imai's style, specifically his famous tarantula with hairy abdomen from waterbomb corrugation. The idea is genius, but the moment I saw the crease pattern, it actually is mad genius. The crease pattern is publicly shared in Jason Ku's Flat Folder instagram. Highly recommend to check it out!

Who would have thought that it is made out of blintzed bird/frog base? Some edges got sunk, then boxpleated to make the thick middle flap into various parts of the cephalothorax and corrugated abdomen. The entire paper was efficiently utilized. It got eyes, fangs, pedipalps, and even spinnerets (appendages at the end of the abdomen) from the frog base's small flaps. The crease pattern was so beautiful that I've stared at it far longer than any others.

Now back to trapdoor spider. To honor of the contest theme, I wanted to make this spider without full-blown boxpleating. The idea was to somehow create accordion from pleats and form a tube, with few flaps inside the tube to be sunk for the abdomen pattern.

Left: side view
Right: top view

The first attempt directly (and shamefully) used something similar to Kota's structure. Maybe we can just sink-in-and-out middle flap of blintzed frog base, and make point split. With tons of edge sinks, maybe it will work. 

Well It didn't, because we can't sink in the middle flap's pointy end and the edges without introducing self intersection. There might be valid ways, but I don't know how. Besides, the middle flap point split is not something I look forward to fold.

I drafted several other layouts, and realized that placing more than 3 legs on an edge yields poor efficiency. We end up with relatively short legs and lots of unused spaces. It was hard to achieve balance of efficiency while producing 8 long legs, 2 pedipalps, and a wide + pleated abdomen.

Explored layouts.

The last (bottom right) stuck on my mind. Basically a bird base with massive extension of pleats. It felt like we could use the long flap as a pair of legs, the short and thick middle flap as abdomen, and fold the rest by boxpleating on the pleats above/below it. The thick middle flap can be made into regular pleats by pushing one layer so it lays beneath the other, a very common technique to make a middle flap behaves like an edge flap. Borrowing Abrashi's terminology, it is called "central flap reconfiguration". 

Central flap reconfiguration converts the thick middle flap's behavior to be like edge flap's.

Can this extended bird base work? Maybe. However we will have to deal with middle flaps above/below the abdomen. This is also closer to a full blown boxpleating.

November ended, and I didn't submit anything.

Actually there was one layout not yet explored: the octagon. Robert Lang's tarantula used this layout where all 8 legs are packed tightly with uniform thickness, and the internal paper is used for cephalothorax, abdomen, and two pedipalps.

While it is an excellent layout for spider in general, I struggled to apply it on this subject. The straight distance inside this octagon is too short to host the pleats for abdomen. I had some ideas to meander it, but nothing was fruitful.

The marked distance is too short for abdomen pleats.

I stopped pursuing this design for the next couple weeks. Perhaps thanks to that mental break, upon coming back I realized that all along there is a part in the crease pattern more suitable for the abdomen pleats: the horizontal symmetry line.

The central part is divided into 20, an arbitrary number.

This line represented by flap B spans almost on the entire paper width. Being more linear, fatter, and longer flap, we could easily squash it in half in case more pleats are needed. This is unlike the radial shape in the first draft. The similarly linear, fat, and shorter flap above it (A) can be used for the abdomen pattern, while the one below it (C) can be split into multiple flaps for pedipalps, fangs, and perhaps eyes.

I made the first test fold with 30 cm masking paper. Even though the abdomen pleats are not enough to fully form a tube (and it might never be, unless rectangular paper is used or we meander the abdomen), we could use the shorter part originally planned for abdomen pattern to cover the bottom half.

To make the abdomen wide, flap B got reverse folded in and out. This is hard to draw in crease pattern as it made the model not flat foldable so I'm not going to draw it.

Even though we've lost the paper for abdomen pattern, we can still salvage the idea by pulling out the buried paper between A and B. Let's try to achieve it by unsinking the part between A and B. This is done by sinking the ridges, then pop out what used to be hinge. I also made the cephalothorax more concrete by making pedipalps and fangs. To prevent interlock between fang and pedipalps, we can use central flap reconfiguration on C. The flaps in the that region ended up behaving like edge flap instead of middle flap.

Left: sink the ridges,
Middle: pop out what used to be hinge, creating a new flap,
Right: fully incorporate central flap reconfiguration.

Another test fold was made. Now it looks more promising. Basically there are 3 layers of pleats to manipulate for the abdomen. The top and bottom will be arched like accordion. The middle one has plenty of paper that can be "sculpted" for the abdomen pattern.

My test fold often end up in messy state

With abdomen and legs set, my attention can be shifted to upgrade the cephalothorax. Currently it has pedipalps and fangs. What's missing is a level shifter to widen the cephalothorax surface. It should be straightforward to add level shifter with "diamond squash", by placing a wide 1 unit flap. The pedipalps were also made 1 unit longer. The grid was increased to 24.

Level shifting, ignoring the bottom half.

Unfortunately it gets tricky to be implemented without producing creases with tiny gap or self intersection on the sunken bottom half. This happened because I did a rational division on an irrational proportion and central flap reconfiguration.

Punishment for mortals dared to mix boxpleating and 22.5 recklessly.

When folded this shouldn't cause any issue. We could have just assumed that there's no gap. However it kind of looks ugly. In the end I shifted this extra gap towards the symmetry line. Now the level shifter creases lie precisely on grid at the cost of tiny gap in the symmetry line. Still ugly, but less.

The tiny green strip goes all the way through the model's symmetry line.
You can see the folded model has tiny gap in the symmetry line.

Thanks to the level shifter the head area is wider. It looks like one end of a pig base. Two of the flaps on the side for fangs now look better, while the one in the center can be folded into eyes. With some experiment I came up with this 4 eyes from squashed edges.

Top: initial version with arbitrary proportion.
Bottom: refined proportion to create equal sized eyes.

The model is ready for another test fold. I made this one with alios kraft just to understand how would this model fare against thin paper. The conclusion was slightly thicker paper would do better to represent the abdomen's volume. In terms of structure it worked pretty well.

Except on the abdomen. Unfortunately the top part is way too long.

Why does it happen? We can analyze the tree structure based on the packing:

Tree is drawn on top right.

I drew the tree upside down to match the crease pattern, so the top part is actually in the bottom. We can see that indeed it is longer than the other two. 

To fix that we need to find a way to slide that part slightly towards the front, without changing any flap length. Finding such transition unit can be difficult. So what I did was something I call "mush legalization". The idea is starting from a flat foldable base, forcefully position the paper towards the goal and flatten. In this case the positioning is a pull on the 2 shorter flaps away from the longer flap. This will cause the longer flap to be shorter, while introducing a river at the base.

Colloquially forcing paper to be flat without precise creases is called mush. However if we look inside the "mush pattern", there are traces of creases that were naturally made to get the base into flat foldable state.

Mush pattern.

These creases can be drawn with adjustment to certain rule (e.g fitted to 22.5 angle), and often a flat foldable transition can be found. I also did this to create wildebeest's mane.

Leftmost: the original.
Everything else: possible solutions.

So there we go, a mush that got legalized. I measured the length on Oriedita and this transition should be enough to align the abdomen correctly. The first solution was picked.

Updated transition to align the abdomen flaps.

Another test fold was made, now with thicker paper: double tissue. The model didn't get too thick and it can still be reasonably shaped. I planned how the abdomen pattern should be made on this test fold. With plenty of pleats to sculpt there should be no problem.

Aligned abdomen.

Showing 3 layers of accordions. The middle one will be sculpted into the abdomen pattern.

Leg Shaping

All my previous arthropods have way fewer joints than actual one. This time I would like to create at least 5 joints per leg, like Kota's. We need are 2 kinds of crimps: upward and downward. These 5 crimps will considerably shorten the leg length.

The upward crimp is easy. We can simultaneously thin and fold it upward with 3D crimp. This is very efficient in terms of minimizing length loss.

This is done on both sides simultaneously.

The downward crimp is more challenging. To provide segmented look, we need to fully pleat the flap, and slide down the paper underneath.

It costs a lot of paper, which I can accept, but the more problematic part is how to do it in the parts close to the body where the flap is thick. Pleating thick flap will cause bulging and the segmented look is not clean. No idea how Kota pulled it off on his fold. My guess is he didn't pleat the entire flap, but rather incorporate internal squash to create pleat forward on top, and pleat backward in the bottom, then finish it with sliding downward. This guarantees the segmented look even on thick part.

Sample x-ray view with 4 layers.
Top: original configuration. Area pointed by arrow is 8 layers thick.
Middle: squash applied on dotted region, pushing the 2nd, 3rd, and 4th layer backward. Area pointed by arrow is 2 layers thick.
Bottom: completed downward crimp with clean segmented look.

How it looks like on crease pattern.
Left: without squash.
Right: with squash.

The drawback is performing the downward slide would be harder. I practiced on the test fold and this should work. This spider has similar proportion as Kota's, with 1 unit long pedipalp and \(1 + \sqrt{2}\) unit long legs so I was confident it can be shaped to mimic his style.

Fold

I used a 50 cm unryu with finely beaten pulp. It is slightly thinner than double tissue so it should ease the leg shaping and provide volume for the abdomen.

Collapsing the base is mostly straightforward. Doing central flap reconfiguration on the cephalothorax and making successive reverse fold for the abdomen's top accordion were the trickiest part. However the biggest blow was shaping the legs as the way they are thinned produce a part with single layer. This is very prone to rip when wet.

Top: cross section of the leg flap.
Bottom: during shaping, the circled part is 1 layer thick while everywhere else is much thicker.

There was no way back though, I had to get all 8 legs thinned and shaped that way. The fear of ripping took away my motivation for months, until one day I made up my mind to finish this model to the bitter end. I had to listen to my work playlist, get into work mode, and begin shaping again.

Initial square.

Precreasing the basic base.

Precreasing the transition. After this, unfold everything and precrease the grid.

Recollapsed after grid precreasing, and now precreasing the sinks.

Sink hell in progress.

Finished central flap reconfiguration.

Improvise, adapt, overcome.

After all these years of origami, aligning face features like eyes or fangs are still difficult

Remarks

On a hindsight this model could have been just made with full blown boxpleating. Also I couldn't replicate Kota's shaping for the legs. May this be experience for future models.

Few weeks ago I got the new origami insect premium book. On every model, the legs are thinned differently: from the uniaxial base, do rabbit ear, and maybe do another fold in half. If applied to this model, the cross section would look like below:

Top: cross section before shaping.
Bottom: after shaping. Circled area is highly stressed but hidden underneath.

This strategy eliminate the single layer problem, but might still be difficult to add crimps. My next arthropod will try to use this strategy.