  Here we study the k^th symmetric trigonometric moment curve and its convex
hull, the Barvinok-Novik orbitope. In 2008, Barvinok and Novik introduce these
objects and show that there is some threshold so that for two points on S^1
with arclength below this threshold, the line segment between their lifts on
the curve form an edge on the Barvinok-Novik orbitope and for points with
arclenth above this threshold, their lifts do not form an edge. They also give
a lower bound for this threshold and conjecture that this bound is tight.
Results of Smilansky prove tightness for k=2. Here we prove this conjecture for
all k.
