Rich Schwartz's eight-vertex paper torus: a flat polyhedral torus embedded in 3-space
In arXiv
.14998 Rich Schwartz proved the existence of an eight-vertex paper torus: a simplicial torus with eight vertices embedded in
R3 with flat triangular faces and total angle
2π at each vertex. This is remarkable because smooth flat tori cannot embed in
R3 — the polyhedral case circumvents this obstruction.
The torus is extremely close to being self-intersecting, making it difficult to visualize. This program renders the mesh directly in
R3, allowing interactive inspection of this delicate geometric object.
Controls: Click and drag to orbit, scroll to zoom.
