I'm creating polygons by stretching strings between numbers on the face of a clock. Those strings represent edges and they create polygons.
I'd like to know how many of those edges, triangles, quadrilaterals (etc.) are distinct.
For instance, in Ex. 1, I get 6 total edges: $$\{0,3\} \{3,6\} \{6,9\} \{9,0\} \{0,6\} \{3,9\}$$
However, only 2 edges are distinct: $|3|$, and $|6|$.
Similarly, I get 4 triangles:
$$\{0, 3, 6\} \{3, 6, 9\} \{6, 9, 0\} \{9, 0, 3\}$$
Yet they are all of the form $(|3|, |3|, |6|)$. Therefore, I have 4 total triangles, and only 1 distinct triangle.
Here's another example.
In Ex. 2, only 3 edges are distinct and only 2 triangles are distinct.
Final example 3, has only 5 distinct edges, and all of its triangles are distinct.
Here's the question: Given the coordinates (on an m-faced clock) of some polygon of n-sides, how can you determine the number of the distinct edges and polygons?