A medical device includes a housing, and a stylet within the housing having a cutting tip upon a stylet shaft. The cutting tip has a plurality of cutting edges in a regular distribution, each being formed by adjoining facets in an alternating arrangement with the cutting edges. The cutting edges are from six to sixteen in number and each slope toward the stylet center axis, such that the cutting tip forms a centrally located point. The facets each have a continuously concave curvature, such that the cutting edges each have a double hollow profile.