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The End of Coins of Constant WidthDragon Curves II

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folding paper folding tube maps london underground platonic solids rhombicuboctahedron raspberry pi weather station programming python php inline code news royal baby probability game show probability christmas flexagons frobel coins reuleaux polygons countdown football world cup sport stickers tennis braiding craft wool emf camp people maths trigonometry logic propositional calculus twitter mathslogicbot oeis pac-man graph theory video games games chalkdust magazine menace machine learning javascript martin gardner reddit national lottery rugby puzzles advent game of life dragon curves fractals pythagoras geometry triangles european cup dates palindromes chalkdust christmas card bubble bobble asteroids final fantasy curvature binary arithmetic bodmas statistics error bars estimation accuracy misleading statistics pizza cutting**2012-10-06 13:14:00**

## 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 | Electromagnetic Field Talk | Tube Map Platonic Solids, pt. 2 | Tube Map Kaleidocycles |

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2015-07-18