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Polyhedra 101: Finding face angles on a tetrahedron?

  1. Apr 12, 2012 #1
    1. The problem statement, all variables and given/known data
    I am trying to find the face angles on a tetrahedron. I have only the base edge lengths, the angles connected the base edges and an (approximate) height of the top/non-base vertex. I might be able to extrapolate other information from images of the base of the tetrahedron, but I'm not quite sure what would be useful.

    For the curious: I'm attempting to determine aerial position from images using known ground landmarks (Fischler-Bolles).

    2/3. Relevant equations and The attempt at a solution
    I'm really looking for an Introduction to the Geometry of a Non-Regular Tetrahedron. I've checked with math libraries, been steered towards Topology, but that's all been mostly not relevant. Everything I've been able to find has been for regular tetrahedrons. Mine is not regular. Pointers to places on the web which would walk me through deriving angles or edge lengths on a non-regular tetrahedron would be VERY much appreciated.

    Many Thanks.
     
  2. jcsd
  3. Apr 12, 2012 #2

    HallsofIvy

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    This is certainly not a trivial problem! What I would do is find the center of two faces having a common edge. Call those P1 and P2. The lines perpendicular to the two centers to that common edge should cross that edge at the same point which I will call E. The three points, P1, E, and P2, form a triangle for which you can calculate the lengths of the sides and so use the cosine law to find the angle at E.
     
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