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Topology

Classifications

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.

Figure 2. Topologically inequivalent shapes. Illustration by Hans & Cassidy. Courtesy of Gale Group.

Figure 3. Topologically inequivalent shapes. Illustration by Hans & Cassidy. Courtesy of Gale Group.

Figure 4. A Möbius strip. Illustration by Hans & Cassidy. Courtesy of Gale Group.

Figure 5. A Klein bottle. Illustration by Hans & Cassidy. Courtesy of Gale Group.

Additional topics

Science EncyclopediaScience & Philosophy: Thallophyta to ToxicologyTopology - Topological Equivalency, Famous Topologists, Classifications, Current Research