Before revision:   Also in higher dimensions, wheel sets turn out to be a suitable model to approach the problem of computing the simplicial depth of a point ~ w in a set ~ H, i.e., the number of simplices spanned by~H that contain~w. While the concept of frequency vectors does not generalize easily, we show how to apply similar methods in higher dimensions .
After revision:  Also in higher dimensions, wheel sets turn out to be a suitable model to approach the problem of computing the simplicial depth of a point ~ w in a set ~ H, i.e., the number of w-embracing simplices. While our previous arguments in the plane do not generalize easily, we show how to apply similar methods in higher dimensions .