Answer
A rectangular solid and a sphere both have the same genus that is zero. No complete cuts can be made without cutting these objects into two pieces.
Work Step by Step
Topology is a modern branch of geometry in which shapes are not assumed to be rigid. The shapes are looked at in a different way. In topology, shapes can be twisted or stretched to form another shape. The objects are classified by the genus of the object.
The total number of full cuts that can possibly be made in any object in order not to split that object into two distinct pieces is called as a genus. Objects having the same genus are referred to be topologically equivalent. For example, a cuboid and a sphere both have the same genus, that is, zero, because the number of cuts that will not split them into two pieces is zero.
