Let \(X\) be a Banach space, and \(X^*\) be its dual. Each cone \(S^*\) of \(X^*\) defines a cone \(S\) in \(X\) via \(S= \{x: f(x)\geq 0\) \(\forall f\in S^*\}\). An operator \(\widehat P\) on a subspace \(V\subseteq X\) is called shape-preserving if \(\widehat P(S\cap V)\subseteq S\). The present paper studies the problem of extending shape-preserving operators. The authors give a characterization of those \(\widehat P\) for which it is necessary and sufficient that \(S^*|_V\) be simplicial in order to admit a shape-preserving extension.