Steme

Steme is a surface-gluing laboratory for quotient-space topology. Start with a unit square, choose how to identify its four edges in pairs, and watch abstract mathematics come alive as a real, interactive surface you can touch and explore. Pick from six canonical gluing presets — Torus, Klein Bottle, Projective Plane (RP2), Sphere, Cylinder, and Mobius Band — or define a fully custom edge-word to discover surfaces of your own. The fundamental polygon redraws in real time as you experiment, giving instant visual feedback on every pairing choice. Switch to Explore mode and drag a token across the square. When it crosses an identified edge it teleports to the paired edge, correctly preserving or inverting orientation depending on the surface. Fire a geodesic snake and watch it wrap continuously, sometimes closing back on itself after traversing a non-orientable boundary. On a Klein Bottle or RP2, the token returns mirror-flipped with its handedness inverted — a behavior that makes abstract topology visceral and immediate. The Classify screen computes the Euler characteristic (V minus E plus F), genus or crosscap number, orientability, and boundary circles, all updated live as you adjust the gluing. A built-in glossary defines twelve core topology terms, each illustrated with a live fundamental-polygon canvas. Save any surface you discover, attach a reference photo, and return to it at any time. No accounts, no logins — all topology mathematics runs on device.