A framework is universally rigid if it is rigid in all higher dimensions. Finding all universally rigid configurations in a given dimension, for a given graph, can be a challenge, even in the line. The answer for a ladder in the line is especially interesting. A ladder is two triangles, the poles, connected by corresponding edges, the rungs. When it flexes, it flexes along the rulings of a flexible hyperboloid in 3-space, and when it is universally rigid it is the orthogonal projection of an orchard ladder (where the pole lines are not parallel) in the plane.

This is joint work with Bryan Chen, Steven Gortler, Tony Nixon, and Louis Theran.