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Poggio
Posts:
2
From:
United States
Registered:
1/16/13


Irregular Pyramids
Posted:
Aug 23, 2013 1:17 PM


I am looking for someone to discuss irregular pyramids. I have developed formulas and methods for finding solutions given only the length of edges.
For an irregular tetrahedron, six lengths assigned to specific edges gives up to one possible solution  formulas for this have been around as early as Piero della Francesca's solution.
For an irregular quadrilateral pyramid, eight lengths assigned to specific edges gives up to four possible solutions. I have developed a formula for this (and don't know of any others). As an example of my "research," the series (14,15,16,17,18,19,20,21) is the smallest series to give a solution for every permutation (5040). Solutions include convex, concave and complex (bowtie) constructions.
For an irregular hexagonal pyramid, eight lengths assigned to specific edges can give many solutions. This is what I'm working on now  finding solutions, graphing and mapping the results. Unfortunately, with 12 edges, the permutations are too large (11! = nearly 40 million) to do an extensive study of any series.
If anyone has any interest in discussion, please feel free to respond.
Message was edited by: Patrick Bell



