What is Vertex figure?
In [[geometry]], a '''vertex figure''' is the [[wikt:figure|figure]] that results when the area around a [[vertex]] (corner) of a [[polyhedron]] or other kind of [[polytope]] is sliced off. The vertex figure of a polytope looks like a shape from the previous [[dimension]]. For example, the vertex figure of a [[cube]] is a [[triangle]]. The shape of a vertex figure on a polyhedron comes from how many of its [[Face (geometry)|faces]] are connected at one vertex. For example, the octahedron has a vertex figure shaped like a square (a four-sided shape) because its vertices each have four triangles connecting together. Besides its number of sides, the exact shape of a vertex figure is different if the faces are meet in a different way. For example, each vertex of a [[cuboctahedron]] has four faces meeting: two triangles and two squares. The polygon faces’ different numbers of sides means that the vertex figure, a [[rectangle]], has two different lengths for its sides. When the vertex figures of one polyhedron have exactly the same shape as the faces of another polyhedron, and the other polyhedron’s vertex figures match the faces of the first polyhedron, the two polyhedra are [[Dual polyhedron|dual]] to each other. {{Math-stub}} [[Category:Geometry]]