I guess that if you perform a crisp linear SVM classifier between two groups, one of it being your data and the other being the null vector, either the algorithm will fail because 0 is in the convex hull of those points (groups not linearly separable), or a solution will be found, where one of the SV will clearly be 0, and the others stay on the surface of the hull nearest to the origin.

I guess that if you perform a crisp linear SVM classifier between two groups, one of it being your data and the other being the null vector, either the algorithm will fail because 0 is in the convex hull of those points (groups not linearly separable), or a solution will be found, where one of the SVs will clearly be 0, and the other k vectors define the k-face of the hull nearest to the origin.