The flowers and leaves/stalks of the potato plant are not edible as they contain solamine since potatoes are part of the nightshade family.
If you want to see potato varieties, PERU! We went in 2011 and in Cuzco, in one of the large bazaars there was 2 full walls, each over 100 ft long, stacked half way up the walls with innumerable kinds of potatoes.
Good to know that they are nightshades, learn something new every day! I'd love to go to Peru someday. Machu Pichu and magical potatoes are on the bucket list!
It is an amazing place. It cost us total about $5k for 2 people for 2 weeks, 1 week each in Cuzco and Arequipa. If you ever get the chance, you have to spend the money on a hotel room at the base of Machu Pichu in Aguas Calientes. You can hike to Machu Pichu or take the bus and stay all day long. We took the train from Cuzco and only got a few hours. My buddy spent a week in Aguas Calientes and had a WAY better experience in the ruins.
Thank you SO much for sharing this advice. That's awesome to know!