For each polygon, I want to get the EdgeIndex of the longest edge (ultimately, I want to get the midpoint of the longest edge for each polygon).

Being literal-minded, I started by getting the length of the longest edge for each polygon:

Here’s a Show Values to show it works:

From there, I hacked my way to the edge index:

The Show Values:

For my second try at getting the index of the longest edge, I stopped trying to go from the length back to the index. I think this is a little better approach: