As part of my research into creating a new side business I went through the process of creating the printable template for constructing a 3D egghead icon, Eggo.
You can see my first attempt here -
I used a Brother Scanncut for doing prototypes - but you can create your own version using this PDF template. If you print it onto card - approx 200gsm and then use a craft knife to cut out the parts.
The red lines are the fold lines so they need scoring. For glue I recommend a tacky PVA glue.
My aim is to eventually produce laser cut kits of animals, things like Owls, sharks, cats, that sort of thing. You can buy lots of templates on Etsy but not many people offer a ready to go kit.