Genus (InstanceTopic, 3)

From Hi.gher. Space

The genus of a shape is equal to how many "holes" it has that fully pierce the shape.

Lines always have a genus of zero. If a hole was created it would be split in half.

There are two types of holes that a shape can have. Pockets are holes completely inside the object and cannot be seen by any outside viewer (unless the being viewing the shape is in a higher dimension than the shape itself). Ordinary holes are ones that can be seen from the outside, for example the hole in a torus. The only type of hole that can be placed inside a polygon is a pocket, as creating a normal hole would split the shape in half.

It is actually debatable that there may be n-1 possible types of holes in any given n-dimensional shape.