 # Icosahedron in OnShape

Inspired by a geodesic planter I saw on Thingiverse, I went about trying to make that shape in OnShape. I thought I might make the same thing out of wood, so I wanted to know what the composite triangle component was, which meant I had to CAD it starting with creating the correct triangular shape. In the end, the CAD was far more fun than I thought trying to make it on a table saw would be, so for now that’s where the project has ended.

I started with a sketch of two pentagons overlaid such that all ten points were equidistant. Then I created that same sketch on a plane some distance above the first. The concept of the shape is that the corner of a triangular side hits a point on a pentagon on one plane and the other two corners hit points on the offset pentagon below.

I wanted to try using variables in OnShape, so I wanted to be able to specify the length of the edge of the triangle and have it regenerate everything to fit together correctly. This meant I needed to calculate the distance between the two planes as a function of the length of the edge of the triangle. It was a fun geometric problem (you can do everything with Pythagoras’ theorem! and angles…) that resulted in a simple factor of the length of an edge as long as I kept the number of sides of the base shape (i.e. 5, a pentagon,) constant. The tricky part in OnShape was getting the edges of the triangle at the correct angle. I ended up creating planes that bisected sketches of where two adjacent triangles would be and using those planes to split and then trim the triangular part. I used the Mid Plane option for creating a plane that bisected two other planes/sketches.

Once I got the correct triangular piece, I could mate them all together to form the shape I wanted.

I don’t think OnShape yet supports linking to public files, but if you’re interested in seeing or messing around the CAD, which is something it supports and I’m really interested in taking advantage of, let me know and I’ll share it with you!