Polygons and Cuboids

Author:
Mr Malkin
Problem 1 Three hexagons fit perfectly around a point. We might describe this setup with the triplet of numbers . What other such triplets of regular polygons fit perfectly around a point? How many such triplets are there? Problem 2 A cuboid has a volume equal to its surface area. What could its dimensions be? How many such cuboids are there? Problem 3 How are the above two problems related?