3ds Max is perfect for this. And has a 30 day FREE trial, with full functionality.
Draw it out in 2D inside 3ds Max. Then simply move the Transform Gizmo to the creases and fold it as you need until you have the desired result. And you can even animate these folds, for added fun.
By "folding" you'll be ROTATING, the currently selected sub selection (those bits you want to fold) around the position of the Transform Gizmo at the crease.
Should be a lot of fun to do, once you figure out all the terminology and techniques of 3ds Max.
3ds Max is probably one of the hardest design apps in the world to learn, but also the most rewarding. And they have some of the best documentation. If you need any particular help coming to terms with it, invest time watching guys use it for polygon modelling on youtube.
And, ironically, 3ds Max is about 10x better for doing 2D design with splines than the specialised 2D software. So that's an added bonus that makes learning how to use it well worthwhile.
Here's the magic feature of 3ds Max. This alone will get you addicted to its way of doing things:
Think of it like an anchor point, but it's MUCH more powerful and freeform than that.
Here's an introduction to Transform Gizmos:
And here's a brief overview of the concept of a Gizmo in 3ds Max:
These things will forever change how you can think of moving things around to create new and interesting shapes.
R is the shortcut key you want most, it's Rotate. Once in this mode, anything currently selected can be rotated around the current position of its transform gizmo.