Hello
I am trying to understand how the option for Rigi works (we won't visit Lucern that day). I would love to include the walk from Rigi Kulm to Rigi Kalbalt too. Is this how I should organise my day?
- Train from Lauterbrunnen to Lucerne (2h 20min) 
- Scenic boat from Lucerne to Vitznau (1h 10min) 
- Cogwheel Train from Vitznau to Rigi Kulm (30 min) 
- Hike to Rigi Kaltbad (1h, mostly downhill???) for scenic views. Better to hike from Kulm to Kaltbad or the other way? 
This is where I am confused. What is the best and nicest way to go back to the train station? Is Rigi Kaltbad going back to Arth-Goldau or only to Weggis? =
- Cogwheel Train from Rigi Kaltbad to Arth-Goldau (30 min) or the cable car from Rigi Kaltbad to Weggis and then the ferry from Weggis back to Lucerne. 
- Train from Arth-Goldau to Lucerne (45 min) 
- Train from Lucerne to Lauterbrunnen (2h 20min) 
Thanks a million