Icosahedron Model, Pedagogically Stretched

Last crawled date: 4 years, 2 months ago

Icosahedron Model, Pedagogically Stretched
i is for Icosahedron (Regular or Platonic)
The present design allows students to make their own Platonic icosahedron models and then play around and within it for mathematical insight such as the three orthogonal golden rectangles. By the way, it spins really well once assembled!
To play with the geometric structure of the icosahedron, one needs some elastic cords such as those for name badges (with some hard end covers), 12 vertices, and 30 edges. The inner edges of the connectors are trimmed for easy assembly.
To assemble the icosahedron, do feel free to press the vertices against some hard surface or use a pair of pliers. Once assembled, it may be hard to take things apart. If so desired, please use the loose vertex or increase the printing resolution. The regular vertex works well in my experiments at 0.18-0.20 mm, 10% infill, with PLA filament.
Among the files
Two versions vertices. The regular one works well at 0.2mm resolution.
Edges of various lengths (50mm to 100mm), which are not to be mixed up. All regular (Platonic) icosahedra are similar to each other, aren't they?
To make an icosahedron, one needs 12 vertices and 30 edges. Here is a simple question to entertain the kids in counting: Each vertex has 5 edges connected to it. There are 12 vertices. So there are 12 * 5 edges. But each edge is shared by two vertices. So there must be 60/2 edges.
References
http://www.froebelweb.org/web7000.html
https://en.wikipedia.org/wiki/Regular_icosahedron