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Mathematical coloring can also be expanded to include three-dimensional graphs. The vertices and edges of polyhedra can be colored using a minimal number of colors.

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 possible.

Consider the following example of vertex and edge colorings of this polyhedra.

Polyhedra without Coloring Vertex Coloring Edge Coloring

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