Pop-up Origami

In my last post, The Final Four-Fold, I presented a minor adjustment to the hopefully mathematically accurate model to describe reflective gravity, or the first step to explain the Theory of Everything. However, in today’s post I take a few steps back. The reason for this is that I realized that when I tried to fit several four-folds together, I saw that the shape of the four-fold means that not all flybys lead to reflections.

If it seems that I’m backtracking from my previous claims, it’s because I am, but just a bit. You see, now it seems that there are two types of reflection four-folds. The first type is the one that I’ve already presented. In this model the flyby paths (marked as edges of yellow and blue triangles) are on the same side of a green (quasi)rectangular plane. The blue paths always end in reflection, whereas the yellow paths end in reflection only half of the time, making them pass the green plane with each flyby.

If you look closely at the above model, you see the second type of reflection four-fold. In it, the blue and yellow triangles are on the opposite sides of the green plane. This means that you must fit both a same-sided folded quadrilateral (cis-isomer, as they say in chemistry) and the opposite-sided folded quadrilateral (trans-isomer) into a unit sphere of reflection.

This means that I need to revise the final four-fold a bit. Nothing dramatic, but for me the change is very concrete. I was hoping that I would include this shape in today’s post, but my initial drafts still look quite messy. I’ll need to work on it more to make the new model presentable.

Perhaps then the reflection model will really be ready. Whether it will or won’t, I’ll only know when I get there.  And finally, why do I call today’s post a popup origami? Well, the above model reminds me of a pop-up book.