To do a coloring for the vertices of a polyhedra, color the vertices so that no two vertices of the same color are connected by a common edge.
To do an edge coloring for a polyhedra, color the edges so that no two edges of the same color meet at a common vertex.
Each of these colorings must be done using the least number of colors
Consider the following example of vertex and edge colorings of this polyhedra.
|Polyhedra without Coloring||Vertex Coloring||Edge Coloring|