vertexconfiguration
Vertex configuration is a concise descriptor used in geometry to name the arrangement of faces that meet at a vertex in a polyhedron or a tiling. It records the cyclic sequence of the face sizes around that vertex, with each number representing the number of sides of a face. The order around the vertex matters, and for uniform structures the same configuration occurs at every vertex.
For example, in a regular tetrahedron three triangular faces meet at each vertex, giving the configuration
Vertex configurations are commonly used to classify regular and semi-regular (Archimedean) solids and uniform tilings, helping