# Genus (InstanceTopic, 3)

### From Hi.gher. Space

In 3D, the **genus** of a shape is equal to how many "holes" it has that fully pierce the shape. For example, a sphere has genus 0, and a torus has genus 1.

In higher dimensions, it gets more complicated: with each new dimension, a new type of hole is possible. So each of the different four-dimensional torii have a pair of numbers as their "genus".

This is closely related to homology groups.