This instructable is a remix of my previous instructable: Platonic Solid Bike Light Fixturehttp://www.instructables.com/id/How-to-make-a-Platonic-Solid-bike-light-fixture/.

The fixture created will fit directly to a Bontrager Glo bike light. They can be purchased on Bontrager's website for around $12.
In this remix, I designed the bottom edge of each platonic solid to act as the fitment disc that I made in the original Platonic Solid instructable. In order to do this though, I had to design the platonic solids from scratch in Rhino CAD, instead of using someone else's platonic solid design.

This instructable with guide you through the steps of how to design the platonic solid bike light fixtures from beginning to end.

You will need: Rhino CAD program, some design skills, and access to a 3D printer.

This specific instructable is only for a dodecahedron, but you can use these methods to make a tetrahedron, octahedron, and hexahedron- you choose!

You can also check out my other instructable for an easier way to make one if you are not as experienced in Rhino or CAD drawing.

Access to a 3D printer is easy if you dont own one, there are companies like Shapeways that will print your design for you and ship it to you!

Step 1:

First, you will need to open Rhino. Make sure the program is set to millimeters, you can change it by going to file>settings>units.
Now, we will begin designing. I'm going to highlight how to design a dodecahedron because it is relatively easy, all you need to know is the dihedral angles of the platonic solid- that is, the angle between each geometric shape that makes up the solid.
For the dodecahedron, the dihedral angle is 116 degrees and 34 minutes.
First, we'll need to make a pentagon that we can copy and angle in relation to itself to begin forming the solid.
To create the pentagon, click on "Polygon: EDGE" and change the number of sides for the polygon to 5.
Click on the edge of the grid, and decide how long you want the edge to be. The edge distance doesn't matter because we'll change the size later.
Now that you have your first pentagon made, we're going to rotate it.
Type "Rotate3D" and press enter. select the polygon, then check the box that says "copy" and select the edge that you are rotate on, in order for it to rotate correctly, click on the left point of the first edge, then the right point of the same edge, press enter, then type in the dihedral angle which is: 116d34' . press enter. Now that you have already done this once, repeat it for each of the edges of the base pentagon, then move to the subsequent edges to create a closed form. 

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