Generation of a laser cuttable geodesic sphere in Grasshopper

Since making my first lamp, I have continued to experiment with parametric geometry and laser cutting. I was inspired by the late Einar Þorsteinn's geodesic domes and Ólafur Elíasson's model room when I saw it at Louisiana last year. Following, I worked out a Grasshopper script that can generate a geodesic sphere, and expanded it so that the rules for generating a geodesic sphere can be applied to more or less, any convex shape. This became the basis for a script that generates a parametric, laser cuttable geodesic sphere.

To generate a geodesic sphere you can start with an icosahedron that contains a sphere. Each triangle face in the icosahedron is subdivided into identical triangular shapes and the triangles are then projected onto the sphere. This results in a network of lines that are called geodesic curves.

The sphere can be further subdivided.

This provides the network of curves that will be the basis of the sphere. Each curve will be extruded into a surface to become a member in the model. To assemble the members, a joint needs to be added where the members meet and slits generated where they meet. 

To visualize the end result, each member is given a thickness. 

The process works on other shapes as well, although the curves can only be regarded as geodesic when the process is applied to a sphere. 

While it proved easy to generate other shapes, I wanted to make a sphere. 

At this point it is trivial to generate the plans for laser cutting. As it turns out there are only 4 types of members in a geodesic sphere, which are easily nested manually by arraying. In order to prevent the laser cutter from doing overlapping cuts due to overlapping curves I must recommend the Topologizer plugin for Grasshopper. 

For this project I decided to go with for this project. They are Copenhagen based and offer a number of different materials, various thicknesses. You just upload a pdf, select a sheet size, press order and a few days later your project arrives by mail. 

So far two of these models have been produced. The one pictured below was produced for a friend who added a light source to it, with quite elegant results.