Spectral geometry
Mini-projects for spectra, geodesics, billiards, and surfaces
A growing collection of small visual databases for geometric objects: exact or enumerated data on lengths, paths, eigenfunctions, and variational surface states.
Compact hyperbolic surfaces
Closed geodesics on compact regular polygon quotients in genera 2 through 5, with opposite-edge identifications in the Poincare disk and upper half-plane models.
- Data
- locally generated side-pairing search
- Status
- symmetry-condensed viewer
Tetrahedron billiards
Inventory of closed billiard trajectories in the regular tetrahedron, with folded and unfolded 3D views.
- Data
- exact and exploratory searches
- Status
- interactive inventory
Closed billiard trajectories
A worked tetrahedron path, the unfolding trick, and the normal-cone rule for singular edge and vertex hits.
- Data
- ordinary and singular examples
- Status
- essay with 3D scenes
Platonic soap-film gallery
Relaxed minimal-surface examples for Platonic wireframes, including live annulus controls.
- Data
- Surface Evolver and relaxed meshes
- Status
- interactive 3D gallery
Arithmetic surface inspector
Prototype manifest for modular orbifold eigenfunction images, geodesic records, and trace-formula diagnostics.
- Data
- manifest-driven records
- Status
- prototype viewer
After M.C. Escher: Edge of infinity
Bend and roam an original four-design reflection tiling in the Poincaré disk and upper half-plane, with procedural detail all the way to the ideal boundary.
- Geometry
- regular hyperbolic {p, q} reflection groups
- Gesture
- scroll, drag, and switch models in place