The given problem requires us to determine the ratio of stars to diamonds based on the given equivalences: one star equals four circles, and three circles equal four diamonds.

Step 1: Understand the problem
To begin solving the problem, let's first understand the information provided. We are given two equivalences:
1. One star is equal to four circles.
2. Three circles are equal to four diamonds.

We need to find the ratio of stars to diamonds. To do this, we will use the given equivalences to establish a relationship between stars and diamonds.

Step 2: Establish the relationship between stars and diamonds
Using the given equivalences, we can establish a relationship between stars and diamonds as follows:
- One star is equal to four circles.
- Since three circles are equal to four diamonds, we can say that one star is equivalent to four circles, which is equivalent to four diamonds.

Step 3: Simplify the relationship
To simplify the relationship, we can divide both sides of the equation by four to find the relationship between stars and diamonds:
- One star is equal to one diamond.

Step 4: Determine the ratio
The ratio of stars to diamonds is 1:1, which means that for every star, there is one diamond.

Step 5: Conclusion
In conclusion, the ratio of stars to diamonds is 1:1. This means that for every star, there is one diamond. The given equivalences allowed us to establish this relationship and determine the ratio.