Stellated polyhedra are three-dimensional geometric shapes formed by extending the faces of a regular polyhedron (a solid with flat faces) beyond their original boundaries until they intersect with each other. The term “stellate” comes from the Latin word “stella,” meaning star and these polyhedra often have a star-like appearance due to their extended faces. They are popular because of their aesthetic qualities. I studied these forms many times before. This time, I implemented the stellations and negative stellations (the excavated polyhedra) of the famous Archimedean Solids in Grasshopper. I used the normal vectors of each face to extrude them. It is a nice and quick exercise of normal vectors and transformations in Grasshopper. You can attach any polyhedra to make their stellated versions, and use the Polyhedra Unroller with Flaps tool to try producing the laser-cutting documents.

This Grasshopper definition generates stellated designs based on the input polyhedra. The input parameters are the type and radius of the base solid and the size of the spikes. It is possible to connect any polyhedra to explore different designs. The output of the definition is the solid 3d model of the design, and it is easy to unroll the faces as polylines. Therefore, it is partially ready for manual cutting or laser cutting. The code is using native Grasshopper components. Thus, no add-ons are necessary for it to work.

You can rebuild the definition by looking at the definition above. However, you will need Archimedean Solids’ vertex coordinates. You can also use the Parakeet add-on to get these solids. However, would you consider being my Patreon if you want to support this website by downloading my working Grasshopper file? Here is the link to my Patreon page, including the Star Polyhedra and more. Thank you.