Scheitelstücke
Scheitelstücke, in geometry often translated as vertex figures, describe the local structure of a polyhedron around a vertex. For a chosen vertex V, a small plane (or equivalently a small sphere centered at V) cuts off the vertex and intersects the edges that emanate from V. The polygon formed by these intersections is the Scheitelstück. Its number of sides equals the number of edges (or faces) meeting at V, and its shape reflects how these faces are arranged around the vertex.
Properties: In regular polyhedra all Scheitelstücke are congruent and are regular polygons; the number of sides
Applications: Vertex figures are used to classify polyhedra and uniform tilings, to infer the Schläfli symbol,
Terminology: In German geometric literature, Scheitelstück is commonly used for the vertex figure; the plural Scheitelstücke