Folding a Truncated Tetrahedron

by Tuğrul Yazar | February 12, 2023 22:41

While digging through the lecture archive, I found this video I made in 2017. We introduce Platonic solids [1]and Archimedean solids[2] in the Design Geometry[3] course at Istanbul Bilgi University. This video shows how we can create an Archimedean solid, the Truncated Tetrahedron[4], 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[5] 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.

Source URL: https://www.designcoding.net/folding-a-truncated-tetrahedron/

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