As far as I can tell each individual resource should have only one canonical path. So in the following example what would good URL patterns be?
Take for an example a rest representation of Companies. In this hypothetical example each company owns 0 or more departments and each department owns 0 or more employees.
A department can't exist without an associated company.
An employee can't exist without an associated department.
Now I'd find the natural representation of the resource patterns to be.
What you have done is correct. In general there can be many URIs to the same resource - there are no rules that say you shouldn't do that.
And generally, you may need to access items directly or as a subset of something else - so your structure makes sense to me.
Just because employees are accessible under department:
Doesn't mean they can't be accessible under company too:
Which would return employees for that company. It depends on what is needed by your consuming client - that is what you should be designing for.
But I would hope that all URLs handlers use the same backing code to satisfy the requests so that you aren't duplicating code.