mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

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:
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...
This is the first post in a series of posts about tube map folding.
Next post in series
Tube map Platonic solids, pt. 2

Similar posts

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

Comments

Comments in green were written by me. Comments in blue were not written by me.
 2017-12-21 
New test comment please ignore
Reply
Matthew
 2015-07-18 
Test comment please ignore
Reply
Matthew
 Add a Comment 


I will only use your email address to reply to your comment (if a reply is needed).

Allowed HTML tags: <br> <a> <small> <b> <i> <s> <sup> <sub> <u> <spoiler> <ul> <ol> <li>
To prove you are not a spam bot, please type "emirp" backwards in the box below (case sensitive):

Archive

Show me a random blog post
 2019 

Sep 2019

A non-converging LaTeX document
TMiP 2019 treasure punt

Jul 2019

Big Internet Math-Off stickers 2019

Jun 2019

Proving a conjecture

Apr 2019

Harriss and other spirals

Mar 2019

realhats

Jan 2019

Christmas (2018) is over
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

draughts trigonometry puzzles a gamut of games braiding error bars dataset asteroids weather station polynomials accuracy light propositional calculus fractals binary python royal baby talking maths in public manchester science festival world cup people maths craft mathslogicbot cambridge dragon curves manchester probability tmip curvature sport plastic ratio noughts and crosses pizza cutting nine men's morris tennis london graph theory football hats map projections video games mathsteroids rugby dates wool machine learning arithmetic interpolation radio 4 pac-man oeis reuleaux polygons triangles speed chalkdust magazine final fantasy frobel european cup programming golden spiral ternary sound captain scarlet folding paper books php go chess news statistics bodmas sorting big internet math-off misleading statistics estimation stickers folding tube maps the aperiodical javascript menace realhats bubble bobble reddit matt parker harriss spiral rhombicuboctahedron chebyshev logic approximation golden ratio coins christmas card martin gardner game of life raspberry pi twitter data christmas inline code london underground platonic solids game show probability flexagons games cross stitch pythagoras gerry anderson mathsjam national lottery hexapawn latex geometry countdown palindromes electromagnetic field

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2019