If, in a plane or spherical convex polygon 
, all of whose sides 
, 
, 
, ..., 
(with the exception of 
) have fixed lengths, one simultaneously increases (decreases)
the angles between these sides, then the length of the variable side increases (decreases).
Steinitz's Lemma
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References
Cromwell, P. R. "Steinitz' Lemma." In Polyhedra. New York: Cambridge University Press, pp. 235-237, 1997.Referenced on Wolfram|Alpha
Steinitz's LemmaCite this as:
Weisstein, Eric W. "Steinitz's Lemma." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SteinitzsLemma.html