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Medial Parallelogram

MedialParallelogram

When a pair of non-incident edges of a tetrahedron is chosen, the midpoints of the remaining 4 edges are the vertices of a planar parallelogram. Furthermore, the area of this parallelogram determined by the edges of lengths d and e in the figure above is given by

A=1/(16)sqrt(4d^2e^2-(b^2+f^2-a^2-c^2)^2)

(Yetter 1998; Trott 2004, pp. 65-66)

See also

Parallelogram

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References

Baez, J. and Barrett, J. W. "The Quantum Tetrahedron in 3 and 4 Dimensions." 16 Mar 1999. http://arxiv.org/abs/gr-qc/9903060.Trott, M. The Mathematica GuideBook for Programming. New York: Springer-Verlag, 2004. http://www.mathematicaguidebooks.org/.Yetter, D. N. "The Area of the Medial Parallelogram of a Tetrahedron." 1 Sep 1998. http://arxiv.org/abs/math.MG/9809007.

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Medial Parallelogram

Cite this as:

Weisstein, Eric W. "Medial Parallelogram." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MedialParallelogram.html

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