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How to make: Platonic solids from tube maps

Impress your friends! As presented in our Talkdust show.


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. 20150716_214907 (1) Fold each map so that two opposite corners meet. In order to make a tetrahedron, each the two pieces must be mirror images. 20150716_214959 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. 20150716_215210 Next unfold both maps. They should fit together to make a tetrahedron. 20150716_21524620150716_215335 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. octahedron

A combination of ten of these pieces (a mixture of both mirror types) will make an icosahedron. 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. cube1 Fold over the overhang. cube2 Fitting the six pieces together will make a cube. 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. dodec-fold1 Next, take one of the parts and fold it into four dodec-fold2 then lay it flat. dodec-fold3 Next, fold the bottom left corner upwards dodec-fold4 and the top right corner downwards. dodec-fold5 Finally, fold along the line shown below. dodec-fold5You 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. dodec-fold5Putting 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. dodec-fold5 Three of the modules attached like this will make a vertex of the dodecahedron. dodec-fold5 By continuing to attach modules, you will get the shell of a dodecahedron. dodec-fold5 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. dodec-fold5

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.

Matthew Scroggs is a PhD student at UCL working on finite and boundary element methods. His website,, is full of maths and now features a video of him completing a level of Pac-Man optimally.
Twitter  @mscroggs    Website    + More articles by Matthew

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2 thoughts on “How to make: Platonic solids from tube maps

  1. Pingback: Enrichment club 02/12/15 | Mr Beckett's A Level Maths

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