Coloring Polyhedra Given by Map Projections

projection

1

2

3

4

5

Dodecahedron

2D

3D

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This Demonstration provides exercises of coloring polyhedra given by map projections using four colors. A proper coloring of a polyhedron

P

colors the faces of

P

so that no two faces that meet along an edge have the same color. According to the four-color theorem, four colors suffice for a planar map or a simply connected polyhedron (one where any closed path on the surface can be contracted to a point).

The first color selected in a column is the one that applies.