  The square-peg problem asks if every Jordan curve in the plane has four
points which are the vertices of a square. The problem is open for continuous
Jordan curves, but it has been resolved for various regularity classes of
curves between continuous and $C^1$-smooth Jordan curves. Here, in a
generalization of the square-peg problem, we consider embedded curves in space,
and ask if they have inscribed quadrilaterals with equal sides and equal
diagonals. We call these quadrilaterals "square-like". We give a regularity
class (finite total curvature without cusps) in which we can prove that every
embedded curve has an inscribed square-like quadrilateral. The key idea is to
use local data to show that short enough arcs have small curvature, thus ruling
out small squares. This allows us to successfully use a limiting argument on
approximating curves.
