To answer your question a bit more detailed I need to explain how triangle to quad works.
I go through the file and if I find a triangle, I search the whole file again for a triangle that has the same ab line. By doing this I rotate the triangle values (abc -> bca -> cab) and if none fits i go to the next line. You can just see that I have to rotate the values one more time to have the same situation as before, but why doing that? it only will costs computing time.
I hope this answers the rest of your question.
I go through the file and if I find a triangle, I search the whole file again for a triangle that has the same ab line. By doing this I rotate the triangle values (abc -> bca -> cab) and if none fits i go to the next line. You can just see that I have to rotate the values one more time to have the same situation as before, but why doing that? it only will costs computing time.
I hope this answers the rest of your question.