  We explore under what conditions one can obtain a nontrivial knot, given a
collection of $n$ vectors. First, we show how to get a crossing from any 3
vectors equal in magnitude, by arbitrarily picking 2 vectors and identifying
the sufficient and necessary criteria for picking a third vector that will
guarantee a crossing when the vectors are reordered. We also show that it's
always possible for a set of vectors to be reordered to form the unknot, if
they sum to $\vec{0}$ when added together.
  Our main results are restricted to sets of $n$ vectors that, when reordered
appropriately, project to a regular $n$-gon in $\mathbb{R}^2$. We prove that if
$n=6$, we cannot form a nontrivial knot with our vectors. The first nontrivial
knot possible ($3_1$) is when $n=7$, and the first $4_1$ knot possible is when
$n=8$. We prove that if $n\geq7$, we can always reorder the vectors to get a
projection of a nontrivial knot, and also provide an algorithm to choose how to
reorder the vectors to get such a knot.
