Geometry : Finding new regular faced polyhedra using Stella

First of all, the Viewer and the Gallery.

As explained in an older post, when working with magnets I end up needing to use Stella software in order to regularize the 3D model made with Blender. The software has two functionalities for that either "Try to make faces regular" or "Create Spring Model". Depending on the model at hand, I try one or the other until I converge to a proper shape. All the matter of this post is to show you how you can obtain new models by playing with other functionalities.

I usually start with an already existing model, let's say an Archimedean solid. Then I can "Augment" similar faces with another polyhedron like a prism or anti-prism and compute the convex hull. At this point, I may have to play with the height coefficient at the augmenting step, especially when having multiple augmentations, otherwise some vertices may be skipped in the hull. The next step is to apply the regularization. It will not always succeed though. The "Spring Model" method constrains the edges to the same length but will not necessarily make the faces flat. The "Face regularization" method constrains flat faces but the edges will not necessarily be of the same length. The end model should have both constraints satisfied, so when flat faces cannot be obtained, they should be replaced by augmenting the model usually with cupolas, prism or antiprism and regularizing the model again. It can take a few iterations and rollbacks to achieve a working model.

I have applied this process to all the Archimedean solids using prism (P) or anti-prism (A). I have named the models using the name of the original solid followed by the letter corresponding to the solid of augmentation. The letter N correspond to not using augmentation (null).

I have also played with other solid and tried to apply some regularization and augmentation processes to them. Please enjoy browsing through the viewer !