This chair is unusual in that it is a cantilever chair, a traditional modernist form first pioneered by the Bauhaus. Cardboard can be very strong, but the cantilever form presents several challenges in using a paper material.
First, the entire chair is essentially in tension: the weight and force of the sitter is pulling on all three of the critical joints, at the floor, the knee, and the junction of the back and the seat. Corrugated cardboard is very strong in compression, when the force is aligned with the grain of the corrugations. However, it has very low tearing strength, especially when the force is perpendicular to the corrugations. I partially overcame this by using the hex cardboard, which is strong in all directions because it has no directional grain.
Second, there are no back legs, meaning the force has to find a path to the ground that is circuitous, winding along the seat to the front legs. The runners along the ground also have to be long enough to prevent the chair form overturning backwards when the sitter leans back. Most cardboard chairs have mass positioned directly under the sitter to add support where there is the most weight.
Last, unlike the cantilever chair featured in my other instructable, this chair only has two legs, instead of a continuous face across the front. To overcome all these structural challenges, it is key that every piece of cardboard become a unified whole. There are no continuous pieces of cardboard; the whole thing is made out of strips, as opposed to cutting out big pieces make the whole profile. The strips are not nearly as strong, and are susceptible to tear-out. The threaded rods at all the critical junctions provide pressure to overcome this tendency.
Step 1: Cut Cardboard
Instead of drafting on paper or in the computer, I just measured out a grid on the floor of my basement and sketched it freehand, full-scale, in chalk. The seat comes to about 14" off the ground. The end of the runners on the floor come even with a vertical line dropped from the top of the back piece. They have to be at least this long to keep the chair from tipping over.
I laid strips over the drawing and cut them with a boxcutter to get all the angles. I marked each one, and they became my templates. For strength, you'll want to overlap each alternating layer, meaning each joint should resemble a log cabin in section as you stack the pieces on top of one another. This also means you'll have to make two different back pieces and two different floor pieces, one short and one long. To save time on all the cutting, I bundled strips together with masking tape, scribed the angles from my templates, and cut them all at once with a handsaw. The last photo shows how strong the cardboard is, supported my weight with just ten inches of corrugated cardboard.