Simplicial Complex
A simplicial complex is a space with a triangulation. Formally, a simplicial complex 
in 
is a collection
of simplices in 
such that
1. Every face of a simplex of 
is in 
, and
2. The intersection of any two simplices of 
is a face of each
of them
(Munkres 1993, p. 7).
Objects in the space made up of only the simplices in the triangulation of the space are called simplicial subcomplexes. When only simplicial complexes and simplicial subcomplexes are considered, defining homology is particularly easy (and, in fact, combinatorial because of its finite/counting nature). This kind of homology is called simplicial homology.
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