  Orbifolds are a modern mathematical concept that arises in the research of
hyperbolic geometry with applications in computer graphics and visualization.
In this paper, we make use of rooms with mirrors as the visual metaphor for
orbifolds. Given any arbitrary two-dimensional kaleidoscopic orbifold, we
provide an algorithm to construct a Euclidean, spherical, or hyperbolic polygon
to match the orbifold. This polygon is then used to create a room for which the
polygon serves as the floor and the ceiling. With our system that implements
M\"obius transformations, the user can interactively edit the scene and see the
reflections of the edited objects. To correctly visualize non-Euclidean
orbifolds, we adapt the rendering algorithms to account for the geodesics in
these spaces, which light rays follow. Our interactive orbifold design system
allows the user to create arbitrary two-dimensional kaleidoscopic orbifolds. In
addition, our mirror-based orbifold visualization approach has the potential of
helping our users gain insight on the orbifold, including its orbifold notation
as well as its universal cover, which can also be the spherical space and the
hyperbolic space.
