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  "body": "\n## Summary\n\nA triangulation of a topological space is a homeomorphism from the geometric realization of a simplicial complex onto the space.\nIt cuts the space into vertices, edges, triangles and their higher-dimensional analogues, glued along faces.\nTriangulations turn topological questions into combinatorial ones, which is how simplicial homology and the Euler characteristic were first computed.\nWhether every manifold can be triangulated, and whether triangulations are essentially unique, are classical questions of geometric topology.\n\n## Explanations\n\n### L1 human\n\nA geodesic dome or a soccer ball made of panels is a sphere cut into flat pieces.\nA triangulation does the same with triangles, and in higher dimensions with tetrahedra and their analogues.\nThe surface of a tetrahedron is a triangulation of the sphere with $4$ vertices, $6$ edges and $4$ triangles.\nThe count $4 - 6 + 4 = 2$ is the Euler characteristic of the sphere, and every triangulation of the sphere gives the same number.\n",
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