In this teaching oriented article, I am introducing the concept of an equilateral rhombus, which is completely characterized. Three main theorems are given with proofs in Section 2. Most of the time, the rhombuses that are discussed are not squares. For a given circle of a specified radius sigma greater than?0, there is exactly one equilateral rhombus unique up to congruence. Cabri II based computer diagrams are used to illustrate these geometrical properties. (Contains 3 figures.)