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For each of the Platonic solids, there is only one dihedral angle, because all pairs of adjacent faces intersect at the same angle.
A vertex of a polyhedron is at the intersection of three or more faces. In the case of three, there is a convenient formula for the dihedral angles. If the three faces fit together at all (they might not), there is only one way. Take this example. Three polygons share the common vertex A. The polygon angles at A are ?, ?, and ?, which are not necessarily equal. The polygons shown here are triangles, but they could have any number of sides.
Start with the faces laid out in a net in a horizontal plane...
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