Building a Dodecahedron

When we say "dodecahedron" we often mean "regular dodecahedron" (in other words all faces are the same size and shape), but it doesn't have to be - this is also a dodecahedron, even  
though all faces are not the same.

Background: You can construct a dodecahedron by cutting 12 identical, regular pentagon faces, beveling all the edges of these to half the dihedral angle and gluing them all together. The joints become the edges. Where 3 faces meet, you have the vertex. Simple enough.Now let's say you want to build a dodecahedron, but instead of boards for the faces, you want the boards to be the edges. Three edges come together at each vertex, etc.

Relative to some dimension of the paper itself, how would you determine/describe the two planes you'd cut at the end of each poster board in order to allow the three poster boards to meet and be correctly oriented in three dimensions? Let's say you want one surface of the board to split the dihedral. (i.e. boards are halfway between being coplanar with the 2 faces on either side.)

References:

Math is Fun! Spinning Dodecahedron

Matematicas Visuales

Paper Models of Polyhedra