Vertex figure

The vertex figure of a polytope, often shortened as verf, is roughly speaking, the section exposed when shaving off a vertex. As such it is the sectioning facet underneath a 0-dimensional element of the polytope. A vertex figure of an n-dimensional polytope is always (n–1)-dimensional. For example, a polyhedron's vertex figure is a polygon, a polychoron's vertex figure is a polyhedron, and so on.