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If $\Delta_{1}$ and $\Delta_{2}$ are abstract simplicial complexes and $\Delta_{1}\subseteq \Delta_{2}$, then we say that $\Delta_{1}$ is a subcomplex of $\Delta_{2}$. Is there a terminology for saying that $\Delta_{2}$ is a $\cdots\cdots$ of $\Delta_{1}$. I want to use the terminology $\Delta_{2}$ is a supercomplex of $\Delta_{1}$, but can find no reference to this or any other terminology for what is a rather basic notion.

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See: math.stackexchange.com/questions/215201/… - I'd go with ambient complex, even though I don't see any reason why you'd wanna use such a notion. –  roman Oct 17 '12 at 10:55
The reason for using such a notion arises from defining a presheaf of abelian groups on a simplicial complex, and then wanting to extend this to the supercomplex continaning it. –  David Ward Oct 17 '12 at 11:03

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