In geometry, a vertex arrangement is a set of points in space described by their relative positions.
A group of polytopes that shares a vertex arrangement is called an army.
For example, the pentagon and pentagram have the same vertex arrangement, while the second connects alternate vertices.
For example, this triangular lattice of points can be connected to form either isosceles triangles or rhombic faces.
For example, of the ten nonconvex regular Schläfli-Hess polychora, there are only 7 unique face arrangements.