Topological shapes are classified according to how many holes they have. Shapes with no holes at all-spheres, eggs, and convex or concave shapes like bowls—are regarded as genus (or type) 0 shapes.
Genus 1 shapes have one hole in them: a donut (or torus), a wedding band, a pipe, or anything with a looped handle (a teacup). Genus 2 shapes have two holes in them, for example, a figure eight. Genus 3 shapes (most pretzels) have three holes in them. And so on.
The determining feature in classifying the topological genus of a shape is deciding if every point in one shape can be transposed or mapped onto a point in the other. Sometimes this process is easy, as in the case of a wedding ring and a donut, which are genus 1 topological shapes. But with complex genus shapes of 4 and above, the determination can be difficult.