I used a computer to produce a prototype because I was not sure that my idea would actually work. I needed to see if the octagon would actually turn out the way that I wanted to. It also gave me what measurements would actually work (i had a couple pages of calculations for ideal measurements).
I used 123D which is great because it is free and easy to use, my next project, which is a secret for now, will also be constructed in that program. I encourage all makers to at least learn how to use CAD(computer aided design) programs as it will come in handy.