  Origami is an ancient art that continues to yield both artistic and
scientific insights to this day. In 2012, Buhler, Butler, de Launey, and Graham
extended these ideas even further by developing a mathematical construction
inspired by origami -- one in which we iteratively construct points on the
complex plane (the "paper") from a set of starting points (or "seed points")
and lines through those points with prescribed angles (or the allowable "folds"
on our paper). Any two lines with these prescribed angles through the seed
points that intersect generate a new point, and by iterating this process for
each pair of points formed, we generate a subset of the complex plane. We
extend previously known results about the algebraic and geometric structure of
these sets to higher dimensions. In the case when the set obtained is a
lattice, we explore the relationship between the set of angles and the
generators of the lattice and determine how introducing a new angle alters the
lattice.
