Geogebra can be downloaded free from https://www.geogebra.org/. You can explore my 3D dodecahedron here: https://www.geogebra.org/m/krkxkqus
Here’s another way to make a dodecahedron: https://youtu.be/B3VRZr3jceY
Here’s some information on how to make shapes from loo roll middles: https://alisonkiddle.co.uk/on-the-twelfth-day-of-christmas-my-true-love-sent-to-me/
Five rooms puzzle: https://en.wikipedia.org/wiki/Five_room_puzzle
Seven bridges of Konigsberg: https://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg