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  "body": "\n## Summary\n\nAn abstract simplicial complex is a family of finite sets closed under taking subsets.\nEach set of size $k + 1$ stands for a $k$-dimensional simplex: a point, a segment, a triangle, a tetrahedron, and so on.\nSimplicial complexes describe spaces by finite combinatorial data, and they link combinatorics with topology and commutative algebra through [[f-vectors and h-vectors|DCK64GFPD7]], homology and Stanley–Reisner rings.\n\n## Explanations\n\n### L1 human\n\nBuild a shape by gluing points, segments, triangles and their higher analogues along common faces.\nRecord each piece by its set of corner labels.\nIf a triangle $\\set{1, 2, 3}$ is in the list, then its edges $\\set{1, 2}$, $\\set{1, 3}$, $\\set{2, 3}$ and its corners must be in the list too.\nThe list of the three corners and the three edges of a triangle, without the triangle itself, describes a loop: the boundary of the triangle.\n",
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