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| Shape | V | E | F | χ | g |
|---|---|---|---|---|---|
| Tetrahedron | 4 | 6 | 4 | 2 | 0 |
| Cube | 8 | 12 | 6 | 2 | 0 |
| Octahedron | 6 | 12 | 8 | 2 | 0 |
| Dodecahedron | 20 | 30 | 12 | 2 | 0 |
| Icosahedron | 12 | 30 | 20 | 2 | 0 |
| Torus (poly) | 16 | 32 | 16 | 0 | 1 |
| Double Torus | 32 | 64 | 32 | -2 | 2 |
Topology is the branch of mathematics that studies properties of spaces preserved under continuous deformations—stretching and bending without tearing or gluing. Often called rubber-sheet geometry, it asks which features of a shape survive when you stretch it into any form: a donut and a coffee mug are topologically the same because each has exactly one hole. This explorer lets you manipulate surfaces interactively, count genus, visualize non-orientable surfaces like the Möbius strip and Klein bottle, and understand why the classification of surfaces is one of topology's great achievements.
topology · continuous deformation · genus · Möbius strip · homeomorphism · Euler characteristic
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