How many ways are there to distictly edge color a set of triangles?

Given a single color, that is the only one you can use to color all edges.

Given two colors, you could use: AAA, AAB, ABB or BBB

Similarly, for 3 colors there are 11 ways (exercise: enumerate the edge colors)

The general rule is: (n**3+2*n)/3

for n=4 we have 24 possibilities: a sizeable number for good puzzles. Reproduced in the following two pages are the 24 triangles with different edges used in place of colors. Print the pages, cut the 24 triangles, and use them as a jigsaw puzzle. There are thousands of ways to arrange the triangles together into a hexagon. Find a few. Particularly pleasing are those where the entire boundary of the big hexagon is made out of one type of edge.