vertex figure

1970, Harold Scott Macdonald Coxeter, Twisted Honeycombs, Conference Board of the Mathematical Sciences, Regional Conference Series in Mathematics: Number 4, American Mathematical Society, page 14, Thus the vertex figure of a polygon is the line-segment whose end-points are the vertex figures of the two edges at one vertex, the vertex figure of a polyhedron or tessellation {p, q} is the polygon {q} whose edges are the vertex figures of the q faces at one vertex, and the analogous "vertex figure" of the honeycomb of cubes (§1) is the polyhedron whose faces are the vertex figures of the eight cubic cells that come together at one vertex.