Simplicial Complex

a Simplicial Complex 𝐾 is a set of simplices that satisfies the following conditions:

• every face of a simplex from 𝐾 is also in 𝐾
• the non-empty intersection of any two simplices 𝜎₁,𝜎₂∊𝐾 is a face of both 𝜎₁ and 𝜎₂

see also the definition of an abstract simplicial complex, which loosely speaking is a simplicial complex without an associated geometry