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Tube map Platonic solids
2012-10-06
This is the first post in a series of posts about tube map folding.
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:
![](javascript:showlimage("tetrahedron.jpg"))
Following this, I folded a cube, an octahedron and an icosahedron:
![](javascript:showlimage("cube.jpg"))
![](javascript:showlimage("octahedron.jpg"))
![](javascript:showlimage("icosahedron.jpg"))
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:
![](javascript:showlimage("fold1.jpg"))
![](javascript:showlimage("fold2.jpg"))
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:
![](javascript:showlimage("cube1.jpg"))
![](javascript:showlimage("cube2.jpg"))
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:
![](javascript:showlimage("dodec.jpg"))
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:
![](javascript:showlimage("tetra.jpg"))
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...
This is the first post in a series of posts about tube map folding.
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⭐ top comment (2017-12-21) ⭐
New test comment please ignoreMatthew
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