After stewing over this for a while, I am still a little confused on finding the dihedral angle between two faces of a regular tetrahedron (problem set 1, part 2, problem #1). I understand explanations I've found on the internet, but still, I am not understanding the explanations (most compute the cross product of two adjacent vectors to get 2 normal vectors; then the angle is computed using the dot product of these two normal vectors). How is this angle the one I am looking for?

Question

After stewing over this for a while, I am still a little confused on finding the dihedral angle between two faces of a regular tetrahedron (problem set 1, part 2, problem #1).  I understand explanations I've found on the internet, but still, I am not understanding the explanations (most compute the cross product of two adjacent vectors to get 2 normal vectors; then the angle is computed using the dot product of these two normal vectors).  How is this angle the one I am looking for?

phi · Answer

the first idea is that a plane is defined by its "normal vector"   this normal is perpendicular to the plane. Parallel planes will have the same normal, but be at different distances from the origin.

the angle between two planes is defined to be the angle between their two normals.
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