Question

When is a rhombus a regular polygon?

Answer 1

A rhombus is never a regular polygon.

Explanation:

A regular polygon must be equilateral (all of its sides are the same length) and equiangular (all of its angles are the same measure). A rhombus is equilateral: all of its sides are of the same length. But it is never equiangular.
A rhombus by definition has two opposite sets of equal angles. It can never, therefore, be equiangular. All of its angles cannot be the same or it would be a square, not a rhombus. A rhombus can never be a regular polygon because it is not equiangular.