Geometry : Making my own polyhedra using Supermag magnets

My encounter with magnetic construction sets was not with the products from the world famous Geomag company but with the Italian brand Supermag from Plastwood. For those of you who know neither one nor the other, a set is a collection of magnetic rods with the same length that you can link together with steel balls to build very simple or complex shapes. Geomag adds flat plastic panels into its set that allows you to easily make basic regular flat polygonal faces. Supermag sets, from the Supermag Magnetic Genius (SMG) collection that I had, came with rods of two different lengths and no panels. The lengths of the rods were chosen so that if you make a square out of the small rods and the balls, a long rod would fit into the diagonal. And conversely, if you make a square out of longs rods, you could strengthen the structure by making a cross inside the square using 4 small rods and a ball. This was their alternative to panels. For bigger structures you could mix up small rods and long rods.

For the record, SMG rods were 25.7mm and 14.4mm long, the balls were 12.7mm in diameter. There were available in six main sets:

Here is a scan of a first leaflet and pictures of the boxes.

Here is a scan of a second leaflet and pictures of the boxes.

In this leaflet, you can see all the different pieces that were part of the Supermag Magnetic Genius sets. You can also see different lines of sets,

I also have a more exhaustive brochure with 36 pages that you can view here.

Finally, this description of SMG sets was just to introduce the fact that it is playing with these little magnets that got me interested into polyhedra with regular faces. The good thing about having a physical model is that you can feel its rigidity and get a sense of its structure. You also get to try many variations around an idea, flipping an edge here, connecting a new vertex there, merging shapes together, etc. I find it very prolific in terms of creativity. I really like this process and having models all around my flat. The downside are numerous: making big models is challenging because the structure can crash under its own weight, the physical body of the pieces may prevent some shapes with small dihedral angles, tolerances in the pieces may make you believe that the mathematical model would work but sometimes it does not. Nethertheless, building shapes with Supermag is a lot of fun.

Regarding the last point, I always make a 3D model on my computer to check its validity. First, I build a topological model with Blender so that the vertices and faces are connected correctly. Then, I export the model to Stella where I can regularize the model so that its edges the same lengths and the faces are flat. Of course, the Stella software use some numerical based algorithm and the final length of the edges is unitary up to the six decimal. This does not serve as a proof that the model is valid, only finding the symbolic coordinates of the vertices would but it is way easier.

Here are all of the polyhedron that I found by playing with my sets:
Viewer and Gallery

Unfortunately, Supermag is much less known than Geomag so finding information and communities is difficult. For completeness, here are links to the websites and forums of the Geomag community:

• [1] the wiki
• [2] the forum
• [3] a website with an impressive collection of pictures of large size models by Rafael Millán

References