Dually, if is a vertex of, then the cone tangent to, with its apex at, touches in a circle, and the system of circles formed in this way are tangent exactly when the vertices they correspond to are connected by an edge.
Dually, if is a vertex of, then there is a cone that has its apex at and that is tangent to in a circle; this circle forms the boundary of a spherical cap within which the sphere's surface is visible from the vertex. The circles formed in this way are tangent to each other exactly when the vertices they correspond to are connected by an edge.