High Quality Content by WIKIPEDIA articles! In geometry, a vertex arrangement is a set of points in space described by their relative positions. They can be described by their use in polytopes. For example a square vertex arrangement is understood to mean four points in a plane, equal distance and angles from a center point. Two polytopes share the same vertex arrangement if they share the same 0-skeleton. The same set of vertices can be connected by edges in different ways. For example the pentagon and pentagram have the same vertex arrangement, while the second connects alternate vertices.