Here are some ideas, pictures and links from a talk given at the annual MathsJam Gathering on 1st December 2019
Have you ever needed a dodecahedron in a hurry? As yet, I haven’t, but if I did, I might consider making something like this:
If you’ve never made one before, James Grime made a nice tutorial video.
It takes a while to make one on your own, but has the advantage that it’s made from readily-available office stationery. You can even make different sized ones and nest them!
If you have slightly more time on your hands, you may wish to consider making something like this:
This took an evening to sew together by hand, once the pieces were cut out.
If you prefer your dodecahedra to be virtual, here’s one made in GeoGebra. Click on the checkbox to remove the pentagons and see what happens when you join the different coloured vertices.
Some of the vertices have been coloured. Untick the checkbox to hide the pentagons and see what happens when you join the coloured vertices…
This is one of my favourite constructions – Five Intersecting Tetrahedra! At Electromagnetic Field in 2018, the Maths Village made a model of it:
You can also make it out of paper. The Mathigon website has some instructions.
Here’s a picture of the one we* made at Talking Maths in Public 2019
(*by “we”, I mean Philipp Legner who folded most of it and assembled all of it, while I helped by holding things. It is HARD to put together. I still haven’t successfully made one on my own.)
Finally, here’s a demonstration of the quickest way I know to make an emergency dodecahedron (this video has no sound):