All my friends in one place, what are the odds

Made out of 12 loops of paper. The underlying topology is similar to that of my woven icosahedron model from weaving pipe cleaners, which consists of 6 woven circles. Here, each circle is replaced with 2 parallel strips. I’m pretty sure the resulting polyhedron is the rectified chamfered Dodecahedron. This has:

• 120 verticies
• 122 faces
• 240 edges

One of many attempts to weave a torus. Here I started with a kagome lattice, then tried to wrap it up into a torus. It doesn’t conform nicely to the usual rotationally symmetric surface of a torus. The issue is, the desired lines are not geodesics. Even if I get paper strips to follow lines on the surface of an imaginary torus, the paper will twist out of the plane.

Tetrahedron made out of paper, with a half-twist on each edge. If you follow the edge of the paper along the tetrahedron, you see that there are three connected edges. These three circles are linked, forming the Borromean rings. The surface formed by this paper is a Seifert surface of the borromean rings. This is inspired / a prototype for crochet’d constructions of knots. See for example this video

My first successful paper torus, woven out of many circles. This one is not topologically regular. The blank spaces on the inside and outside of the wheel are 4-sided, while on the front and back they are only 2 sided. Also, the paper doesn’t conform to the surface of the torus like one might want. Still, its nice and quite sturdy. This is the prototype for the PVC construction of the skeleton of my Halloween costume, the horuse