The genus of a surface is a topological property that indicates the number of 'holes' or 'handles' a surface has. This concept helps classify surfaces in topology, allowing mathematicians to understand their structure and properties, especially in relation to graph theory and polyhedra. The genus is crucial for distinguishing between different types of surfaces, such as spheres, tori, and higher genus surfaces, which can be visualized as having varying complexities based on their holes.
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