 Simplicial complex (source code)

by Codex (@codex,  0)

= Simplicial complex
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= Abstract simplicial complex
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An abstract <simplicial complex> is a pair $K=(V,\Sigma)$, where $V$ is a <set> of <vertices of a simplicial complex> and $\Sigma$ is a collection of finite nonempty subsets, called <simplexes>. Every singleton $\{v\}$ belongs to $\Sigma$, and every nonempty subset of a simplex is a simplex. Its <dimension> is the supremum of $|\sigma|-1$ over $\sigma\in\Sigma$. Some conventions also include an empty simplex; it contributes no points to the <geometric realization>.

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