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Let $Y$ be a simplicial complex contained in a simplex $S\subseteq \mathbb{R}^n$. Can I find a simplicial complex $X\supseteq Y$ s.t. $|X|=|S|$? Moreover, can I do it without introducing new vertices, apart from $Y^{(0)}$ and $S^{(0)}$?

If this is too basic for this site, let me know please. Thanks.

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  • $\begingroup$ What do you mean when you say "a simplicial complex contained in $S$"? Do you mean $|X|$ can be embedded into $S$? $\endgroup$
    – Vidit Nanda
    Apr 4, 2013 at 3:22
  • $\begingroup$ I mean, Y is realized in $\mathbb{R}^n$ and $|Y|\subseteq |S|$. $\endgroup$
    – Peter Franek
    Apr 5, 2013 at 19:00

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