This post contains instructions for how to make Platonic solids from tube maps or other leaflets, as I have talked about at Talkdust and other events.
Platonic solids with triangular faces
First, to make a tetrahedron, take two tube maps and fold the covers over to the back. This will allow the map itself to appear on the faces of the solid instead of the cover. Fold each map so that two opposite corners meet. In order to make a tetrahedron, each the two pieces must be mirror images. Now fold the overhangs over to make each map into a triangle. After these folds, only parts of one page of the map should be visible. Next unfold both maps. They should fit together to make a tetrahedron. The edge of each map should have gaps between pages. Tuck the overhangs into these to make the shape more sturdy.
To make an octahedron, make four identical pieces as above (these should not be mirror images) and fit them together.
A combination of ten of these pieces (a mixture of both mirror types) will make an icosahedron.
Platonic solids with square faces
To make a cube, fold the covers of six tube maps over (again this ensures that the cube’s faces will be map not cover). Place pairs of tube maps on each other at right angles. Fold over the overhang. Fitting the six pieces together will make a cube.
Platonic solids with pentagonal faces
To make a dodecahedron, take a tube map, cut apart all the pages and cut each page in half. Next, take one of the parts and fold it into four then lay it flat. Next, fold the bottom left corner upwards and the top right corner downwards. Finally, fold along the line shown below. You have now made a module which will make up one edge of the dodecahedron. You will need 30 of these to make the full solid. Putting it Together Once many modules have been made, then can be put together. To do this, tuck one of the corners you folded over into the final fold of another module. Three of the modules attached like this will make a vertex of the dodecahedron. By continuing to attach modules, you will get the shell of a dodecahedron. To make the dodecahedron look more complete, fold some more almost-squares of tube map to be just larger than the holes and tuck them into the modules.
Other stuff to do
Of course, you could make Platonic solids with paper other than tube maps:
Or you could try making other solids:
If you make some Platonic (or other) solids, be sure to share them with us on Twitter.
More from Chalkdust
- Matthew Scroggs sets the first puzzle. Can you solve it?
- Did you solve it?
- Did you solve it?
- We have a go at the puzzles in Daniel Griller’s new book
- Win £100 of Maths Gear goodies by solving our famously fiendish crossnumber
- Find out more about the spiral trees on the cover of Issue 09