Vertex-decomposability is just zero-decomposability when S is pure, see [PB]. When S is non-pure, [BW-2] gives a generalisation: A complex S is vertex decomposable if it is either a simplex or there exists a shedding vertex.
i1 : R = QQ[a..f];
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i2 : isVertexDecomposable simplicialComplex {a*b*c*d*e}
o2 = true
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i3 : isVertexDecomposable boundary simplicialComplex {a*b*c*d*e}
o3 = true
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i4 : isVertexDecomposable simplicialComplex {a*b*c, c*d*e}
o4 = false
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i5 : isVertexDecomposable simplicialComplex {a*b*c, c*d, d*e, e*f, d*f}
o5 = true
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Whether the complex is vertex-decomposable is cached.