A Theorem on the Dihedral Angles of a Tetrahedron
A Theorem on the Dihedral Angles of a Tetrahedron
Let , , , , , be the edges of a tetrahedron and let , , , , , be the corresponding dihedral angles. Define the function on pairs of opposite edges and dihedral angles as ++2pqcotp'cotq', where is the dihedral angle at and is the dihedral angle at .
a
b
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α
β
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δ
ϵ
ϕ
p⊗q
2
p
2
q
p'
p
q'
q
A theorem states that this function is constant on the three pairs of opposite edges of a tetrahedron.