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## Tube map Platonic solids

This week, after re-reading chapter two of

*Alex's Adventures in Numberland*(where Alex learns to fold business cards into tetrahedrons, cubes and octahedrons) on the tube, I folded two tube maps into a tetrahedron:Following this, I folded a cube, an octahedron and an icosahedron:

The tetrahedron, icosahedron and octahedron were all made in the same way, as seen in

*Numberland*: folding the map in two, so that a pair of opposite corners meet, then folding the sides over to make a triangle:In order to get an equilateral triangle at this point, paper with sides in a ratio of 1:√3 is required. Although it is not exact, the proportions of a tube map are close enough to this to get an almost equilateral triangle. Putting one of these pieces together with a mirror image piece (one where the other two corners were folded together at the start) gives a tetrahedron. The larger solids are obtained by using a larger number of maps.

The cube—also found in

*Numberland*—can me made by placing two tube maps on each other at right angles and folding over the extra length:Six of these pieces combine to give a cube.

Finally this morning, with a little help from the internet, I folded a dodecahedron, thus completing all the Platonic solids:

To spread the joy of folding tube maps, each time I take the tube, I am going to fold a tetrahedron from two maps and leave it on the maps when I leave the tube. I started this yesterday, leaving a tetrahedron on the maps at South Harrow. In the evening, it was still there:

Do you think it will still be there on Monday morning? How often do you think I will return to find a tetrahedron still there? I will be keeping a tetrahedron diary so we can find out the answers to these most important questions...

### Similar posts

Tube map Platonic solids, pt. 3 | Tube map Platonic solids, pt. 2 | Tube map kaleidocycles | Tube map stellated rhombicuboctahedron |

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2017-12-21^{comment}pleaseignoreMatthew