Those Menger cube models are interesting. Is there any way to make a paper Sierpinski tetrahedron?
I've made paper models of the
Platonic,
Archimedean and
Kepler-Poinsot solids with the designs on
this site back when it had much less.
It is possible to make models like those with origami, especially modular origami. The ones I did were with tabs and glue.
Those got crushed when I was away at RIT.

So I plan on making new ones using a program to print out the designs for those again plus a lot more such as the
Catalan solids, some
prisms, some
antiprisms, the rest of the
uniform polyhedra, the
uniform compounds,
Johnson solids and some other groups as well as tilings in two and three dimensions. Then once I have those taken care of, there are the four dimensional ones, which includes six convex regular shapes as opposed to only five such polyhedra in three dimensions and an infinite number of regular polygons in two dimensions. Then there are the higher dimensions

with three convex regular shapes each and many nonconvex ones.
The some of the nonconvex snub polyhedra uniform compounds of their mirror images are each going to take a while to make. On the bottom of
this page, George Hart says if someone makes a paper model of the compound of the mirror images of the great inverted retrosnub icosidodecahedron, he would buy them a beer.

His
site is a nice introduction to this topic. It is also known as UC72, or the 72nd uniform compound.
From what I've read, at least two models of this exist in the world, so maybe mine could be the third one.

It's going to be hard because the self-intersecting faces of such polyhedra cut each other into little pieces and notches that could be as small as millimeters across even when the whole thing is around a meter across. I figured that the pieces for that one would take up around 350 pages if I printed out the most effective arrangement of parts I was able to get in the program. So, I may print out one instance of each part and use those to make duplicates that don't leave lots of empty paper.
I tried to count up most of what is on my list of what to build and it ended up being over 500 items. I'm sure it'll go way over that, maybe over 1000. Only a few of them really need to be large to be fully detailed. Most of them can be made small and should fit into my room.

I've had practice cutting small things with my exacto knife for another project and got a book from the library about shelves, so I could get ideas about what to design to store all of these things.

It all started with another book from the library, Shapes, Space and Symmetry, which showed how a lot of those are related to each other.