Geometry : Discovery of Lobel Frames
Created on August 8, 2022. Last update on August 10, 2022.
Lobel frames are a set of polyhedra which faces are only made of equilateral triangles. It was studied by the French architect Alain Lobel whose aim was to create buildings with various shapes from the same triangular panel. Long story short, he was able to write programs that would help him find many such shapes that he has categorized into 9 different families. I vividly encourage you to take a look at his website which is still running and provides (in English and French) many details about his work [1].
Alain Lobel passed away 15 years ago. I was able to get into contact with his family which was managing the website and I got the authorization to access most of the digital archive of his work. My intent is to bring a new light onto his work to the world. In this post, I will start by showing quickly the categories and the models using the polyhedra viewer. In further posts, I will try to analyse the algorithms that were used to generate the models. I'll need to learn Basic on the way though so it may take some time.
Lobel Frames are classified into 9 categories, two of which form open shapes: C3 and C6. The other 7 forms closed volumes. Here they are:
Viewers
It may take some time to load depending on your machine but here is the viewer with all 9 categories and 1716 models at once, enjoy !
Galleries
There may be up to several hundred of models on a single page. It displays well on my computer, hope it does the same on yours.
References
[1] Alain Lobel. Lobel Frames. https://www.equilatere.net. Accessed on 08-10-2021.
