When you work with foam, you need to think 3 dimensionally. The template you use from Pepakura is in 2 dimension. When you translate that to foam, you are dealing with another face (depth of the foam).
To hide the edges, you need to cut at an angle, as previously mentioned in my earlier post. Let me illustrate with a quict 3D image I put together.
If you do it correctly, it shoud look like this.
Hope that helps.