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geometryangle

How to know if a dihedral angle is + or -?


In several posts post1 and post2 have been shared how to obtain a dihedral angle with four points or their two planes. But ... How can one know if that dihedral angle is positive or negative?

  • What I have in mind to clasify them is the following diagram:

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Solution

  • Calculate triple product of vectors P1P2, P2P3 and P3P4.

    Sign of the value of this triple product shows handedness of vector triplet (right-handed or left-handed) and corresponds to the sign of dihedral angle