While digging through the lecture archive, I found this video I made in 2017. We introduce Platonic solids and Archimedean solids in the Design Geometry course at Istanbul Bilgi University. This video shows how we can create an Archimedean solid, the Truncated Tetrahedron, by folding it from a flat sheet.
While doing this, I intersected the spheres by using the relations between the side lengths of the solid, and I calculated the rotation angles accordingly. First of all, I drew the unfolded net of the Truncated Tetrahedron. Then, I found the rotation circle of the outer vertex of one of the triangular faces. For this, I intersected two spheres from opposite vertices. Next, I repeated the same process for one of the neighboring hexagon faces. After I found its circle of rotation, I intersected these two circles. The resulting point forms the point where I will rotate the triangular and hexagonal faces and snap them. After I found this rotation angle, I rotated the other faces accordingly and closed the shape. In addition to folding a Truncated Tetrahedron, the same method can be used to fold other solids.

For those who are interested in the construction of a Truncated Tetrahedron by literally truncating a tetrahedron, this post can be useful.

It is a good exercise both for learning the basic uses of Rhino software and for using the problem-solving steps when constructing a geometric object. But the video is a bit boring and old. Unfortunately, the image quality of the video is also not very good. I assume that in the future I can shoot videos with better quality and sound. Have to deal with it for now. Maybe in the future, somebody can re-shoot these.