Steffen's Polyhedron – Greg Egan

Author and physicist Greg Egan explores the mathematical properties of Steffen's polyhedron, a famous example of a flexible polyhedron. Unlike rigid solids, a flexible polyhedron can change its shape without deforming its faces. Steffen's polyhedron is notable for being the simplest known example of such a shape, consisting of only nine vertices and fourteen triangular faces. Egan provides a detailed analysis of the geometry behind this object, including the mathematical proofs regarding its non-rigid nature and the constraints that allow it to move without self-intersection. The article serves as a deep dive into the intersection of geometry and topology, offering readers a clear explanation of how these complex structures function. By breaking down the vertices and edges, Egan illustrates the elegance of this geometric curiosity, making advanced mathematical concepts accessible to those interested in the fundamental principles of shape and space.