If 
is a subcollection of a simplicial complex 
that contains all faces of its elements,
then 
is another simplicial complex called a simplicial
subcomplex.
Simplicial Subcomplex
See also
Simplicial ComplexExplore with Wolfram|Alpha
References
Hatcher, A. Algebraic Topology. Cambridge, England: Cambridge University Press, 2002.Munkres, J. R. Elements of Algebraic Topology. New York: Perseus Books Pub., 1993.Referenced on Wolfram|Alpha
Simplicial SubcomplexCite this as:
Weisstein, Eric W. "Simplicial Subcomplex." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SimplicialSubcomplex.html