I couldn't find any accurate models of the 2009 and 2013 Star Trek reboot badges to wear to the opening showing. I found some good photos of official prop replicas and got measurements of one, traced them in Inkscape, exported as DXF and used OpenSCAD to extrude them and export them to STL.
Warm and bend (optional)
Fill & Sand (optional)
Primer & Paint
Adhere to your left chest with double-sided tape (as was done on set)