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We know the coordinates of the vertices and the color of each part, e. g. in such a way Graphics[{EdgeForm[Black], Red, Polygon[{{0, 0}, {0, 2}, {2, 2}, {2, 1}, {3, 1}, {3, 2}, {4, 2}, {4, 0}}], EdgeForm[Black], Green, Polygon[{{0, 2}, {0, 6}, {3, 6}, {3, 4}, {2, 4}, {2, 5}, {1, 5}, {1, 3}, {2, 3}, {2, 2}}], EdgeForm[Black], Blue, Polygon[{{1, 3}, {1, 5}, {2, 5}, {2, 3}}], EdgeForm[Black], Red, Polygon[{{3, 2}, {3, 6}, {5, 6}, {5, 2}}], EdgeForm[Black], Green, Polygon[{{2, 1}, {2, 4}, {3, 4}, {3, 1}}], EdgeForm[Black], Green, Polygon[{{4, 0}, {4, 2}, {5, 2}, {5, 0}}]}].

Addition. The following result in green

is not a polygon so is not allowed.

We know the coordinates of the vertices and the color of each part, e. g. in such a way

Graphics[{EdgeForm[Black], Red,  Polygon[{{0, 0}, {0, 2}, {2, 2}, {2, 1}, 
    {3, 1}, {3, 2}, {4, 2}, {4, 0}}], 
 EdgeForm[Black], Green,    Polygon[{{0, 2}, {0, 6}, {3, 6}, {3, 4}, {2, 4}, 
    {2, 5}, {1, 5}, {1, 3}, {2, 3}, {2, 2}}], 
 EdgeForm[Black], Blue, Polygon[{{1, 3}, {1, 5}, {2, 5}, {2, 3}}], 
 EdgeForm[Black], Red, Polygon[{{3, 2}, {3, 6}, {5, 6}, {5, 2}}],
 EdgeForm[Black], Green, Polygon[{{2, 1}, {2, 4}, {3, 4}, {3, 1}}], 
 EdgeForm[Black], Green, Polygon[{{4, 0}, {4, 2}, {5, 2}, {5, 0}}]}]

Addition. The following result in green is not a polygon so is not allowed:

Let a partition of a planar polygon into colored polygons be given, i.e. something similar to

We know the coordinates of the vertices and the color of each part, e. g. in such a way Graphics[{EdgeForm[Black], Red, Polygon[{{0, 0}, {0, 2}, {2, 2}, {2, 1}, {3, 1}, {3, 2}, {4, 2}, {4, 0}}], EdgeForm[Black], Green, Polygon[{{0, 2}, {0, 6}, {3, 6}, {3, 4}, {2, 4}, {2, 5}, {1, 5}, {1, 3}, {2, 3}, {2, 2}}], EdgeForm[Black], Blue, Polygon[{{1, 3}, {1, 5}, {2, 5}, {2, 3}}], EdgeForm[Black], Red, Polygon[{{3, 2}, {3, 6}, {5, 6}, {5, 2}}], EdgeForm[Black], Green, Polygon[{{2, 1}, {2, 4}, {3, 4}, {3, 1}}], EdgeForm[Black], Green, Polygon[{{4, 0}, {4, 2}, {5, 2}, {5, 0}}]}].

How to write a Mathematica program which unites the polygons having a joint edge and the same color into a single simple polygon, not a polygonial figure (see Encyclopedia of Mathematics and Wiki)? For the above partition we have to obtain two green polygons, one red polygon, one yellow polygon, one blue polygon, and one violet polygon.

Addition. The following result in green

is not a polygon so is not allowed.

Let a partition of a planar polygon into colored polygons be given, i.e. something similar to

We know the coordinates of the vertices and the color of each part, e. g. in such a way Graphics[{EdgeForm[Black], Red, Polygon[{{0, 0}, {0, 2}, {2, 2}, {2, 1}, {3, 1}, {3, 2}, {4, 2}, {4, 0}}], EdgeForm[Black], Green, Polygon[{{0, 2}, {0, 6}, {3, 6}, {3, 4}, {2, 4}, {2, 5}, {1, 5}, {1, 3}, {2, 3}, {2, 2}}], EdgeForm[Black], Blue, Polygon[{{1, 3}, {1, 5}, {2, 5}, {2, 3}}], EdgeForm[Black], Red, Polygon[{{3, 2}, {3, 6}, {5, 6}, {5, 2}}], EdgeForm[Black], Green, Polygon[{{2, 1}, {2, 4}, {3, 4}, {3, 1}}], EdgeForm[Black], Green, Polygon[{{4, 0}, {4, 2}, {5, 2}, {5, 0}}]}].

How to write a Mathematica program which unites the polygons having a joint edge and the same color into a single polygon with the simply-connected interior, not a polygonial figure (see Encyclopedia of Mathematics and Wiki)? For the above partition we have to obtain two green polygons, one red polygon, one yellow polygon, one blue polygon, and one violet polygon.

Addition. The following result in green

is not a polygon so is not allowed.

Let a partition of a planar polygon into colored polygons be given, i.e. something similar to

We know the coordinates of the vertices and the color of each part, e. g. in such a way Graphics[{EdgeForm[Black], Red, Polygon[{{0, 0}, {0, 2}, {2, 2}, {2, 1}, {3, 1}, {3, 2}, {4, 2}, {4, 0}}], EdgeForm[Black], Green, Polygon[{{0, 2}, {0, 6}, {3, 6}, {3, 4}, {2, 4}, {2, 5}, {1, 5}, {1, 3}, {2, 3}, {2, 2}}], EdgeForm[Black], Blue, Polygon[{{1, 3}, {1, 5}, {2, 5}, {2, 3}}], EdgeForm[Black], Red, Polygon[{{3, 2}, {3, 6}, {5, 6}, {5, 2}}], EdgeForm[Black], Green, Polygon[{{2, 1}, {2, 4}, {3, 4}, {3, 1}}], EdgeForm[Black], Green, Polygon[{{4, 0}, {4, 2}, {5, 2}, {5, 0}}]}].

How to write a Mathematica program which unites the polygons having a joint edge and the same color into a single polygon? For the above partition we have to obtain two green polygons, one red polygon, one yellow polygon, one blue polygon, and one violet polygon.

Addition. The following result in green

is not a polygon so is not allowed.

Let a partition of a planar polygon into colored polygons be given, i.e. something similar to

We know the coordinates of the vertices and the color of each part, e. g. in such a way Graphics[{EdgeForm[Black], Red, Polygon[{{0, 0}, {0, 2}, {2, 2}, {2, 1}, {3, 1}, {3, 2}, {4, 2}, {4, 0}}], EdgeForm[Black], Green, Polygon[{{0, 2}, {0, 6}, {3, 6}, {3, 4}, {2, 4}, {2, 5}, {1, 5}, {1, 3}, {2, 3}, {2, 2}}], EdgeForm[Black], Blue, Polygon[{{1, 3}, {1, 5}, {2, 5}, {2, 3}}], EdgeForm[Black], Red, Polygon[{{3, 2}, {3, 6}, {5, 6}, {5, 2}}], EdgeForm[Black], Green, Polygon[{{2, 1}, {2, 4}, {3, 4}, {3, 1}}], EdgeForm[Black], Green, Polygon[{{4, 0}, {4, 2}, {5, 2}, {5, 0}}]}].

How to write a Mathematica program which unites the polygons having a joint edge and the same color into a single simple polygon, not a polygonial figure (see Encyclopedia of Mathematics and Wiki)? For the above partition we have to obtain two green polygons, one red polygon, one yellow polygon, one blue polygon, and one violet polygon.

Addition. The following result in green

is not a polygon so is not allowed.