The issue is with the "sheet of paper" concept. Spoilers ahead.
In the story, a two-dimensional plane is shot into the solar system and as it interacts with three-dimensional matter, it converts the three-dimensional matter into two dimensions. The author describes that the shapes of the three dimensional objects are "unfolded" onto the two-dimensional plane - that no surface is hidden. The author also indicates that the shape of objects, such as people remain recognizable.
Three sections from the book:
It was possible to distinguish every individual on Revelation: They were laid out side by side, holding hands, every single cell in their body exposed to space in two dimensions.
Both gas giants had been two-dimensionalized. Uranus’s orbit was outside Saturn’s, but since Uranus was currently on the other side of the Sun, Saturn had fallen into the two-dimensional plane first. The giant planets ought to look like circles after collapsing, but due to the angle of view from Pluto, they appeared as ovals.
The precision of the drawing was at the level of the individual atom. Every atom in the original three-dimensional space was projected onto its corresponding place in two-dimensional space according to ironclad laws. The basic principles governing this drawing were that there could be no overlap and no hidden parts, and every single detail had to be laid out on the plane.
The problem is that if the unfolding occurs down to the atomic scale and the plane is truly two dimensions (which it is described as having zero/non distinguishable height), then the individual atoms have to unfold. An atom unfolding its internal shapes would be massive. The author has already established the behavior in the first book, The Three Body Problem, when the Trisolarans unfolded a proton which filled their sky:
The second try unfolds the proton into three dimensions, and large, reflective geometric solids fill the sky, “as though a giant child had emptied a box of building blocks in the firmament,”
Due to this, I believe if an object were to unfold at the atomic level - first it would not be recognizable on the two-dimensional plane and secondly would take up a massive portion on the plane. I don't have the math, but my guess is that an object such as a spaceship would occupy a two-dimensional plane much larger than the solar system.
We can do a simple thought experiment:
Let's say we have a three-dimensional cube that is made up of two-dimensional sides (the sides have no thickness, only length and width). Unfolding the cube to two dimensions, we see six two-dimensional sides. But, we also have to account for the other sides of the two-dimensional sides, meaning there are now twelve "sides" on our two-dimensional plane. For complex objects, you can see how this would get significantly more complicated and the shapes' areas on the place would get exponentially larger. Getting down to the atomic level (because atoms are three dimensional) and the scale would be unfathomable.
And I believe the same would happen in reverse. If a 3D object was to go into 4D space, I believe the scale effect would occur in the opposite direction. An object would become infinitely smaller - but when the spaceship (I forgot the name) entered 4D space, for all intents and purposes, it remained the same/unchanged.
All that said, am I correct in this hypothesis? And at the very least, is there an issue with Cixin Liu's world building between the size of the Sophons and the effect on converting three-dimensional elements to two dimensions?