In modern computational geometry and aerospace engineering, origami is the mathematics of deployable space structures, cardiac stents, and non-Euclidean metamaterials.
The Four Authentic Manifolds:
- Miura-ori: Invented by Japanese astrophysicist Koryo Miura in 1970 to pack solar panel arrays into rocket fairings with rigid parallelogram facets.
- Yoshimura Diamond Pattern: Discovered in thin-walled cylindrical rocket shells under axial compression, buckling into triangular diamond cells.
- Ron Resch Triangular Dome: Architectural folding tessellation that morphs a flat sheet into curved 3D geodesic space.
- Corpus Hypercubus Net: Salvador Dalí's 8-cube 3D cross net folding outward into a 4-dimensional tesseract.
Kawasaki's Theorem: At every flat-foldable degree-4 vertex, the sum of alternating sector angles equals $180^\circ$.