Five Over Five, a summer exhibition of the Lehigh Art Alliance top five award winners from the past five years.

A simplicial arrangement of pseudolines is a collection of topological lines---that is, a collection of curves where each pair intersects exactly once---in the projective plane where each region that is formed is triangular. This talk will discuss a kaleidoscope construction to produce symmetric pseudoline arrangements, and it will show how to use this construction to produce and analyze several infinite families of simplicial pseudoline arrangements with high degrees of geometric symmetry. Many pretty pictures will be provided.

We will explore some of the exciting recent history of the study of polyhedra and polytopes, in particular efforts to generalize the theory to the study of non-convex bodies. Our discussion will include topics such as the recently solved Bellows Conjecture, the realizability of flexible polyhedra, approaches for generalizing polytopes to non-convex bodies in higher dimensions, and some ways in which intuition based on the study of polyhedra doesn't necessarily extend to higher dimensions.