mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

Tube map kaleidocycles

 2016-09-06 
This is the fifth post in a series of posts about tube map folding.
After my talk at Electromagnetic Field 2014, I was sent a copy of MC Escher Kaleidocycles by Doris Schattschneider and Wallace Walker (thanks Bob!). A kaleidocycle is a bit like a 3D flexagon: it can be flexed to reveal different parts of itself.
In this blog post, I will tell you how to make a kaleidocycle from tube maps.

You will need

Making the modules

First, fold the cover of a tube map over. This will allow you to have the tube map (and not just its cover) on the faces of your shape.
With the side you want to see facing down, fold the map so that two opposite corners touch.
For this step, there is a choice of which two corners to connect: leading to a right-handed and a left-handed piece. You should make 6 of each type for your kaleidocycle.
Finally, fold the overhanding bits over to complete your module.
The folds you made when connecting opposite corners will need to fold both ways when you flex your shape, so it is worth folding them both ways a few times now before continuing.

Putting it together

Once you have made 12 modules (with 6 of each handedness), you are ready to put the kaleidocycle together.
Take two tube maps of each handedness and tuck them together in a line. Each map is tucked into one of the opposite handedness.
The four triangles across the middle form a net of a tetrahedron. Complete the tetrahedron by putting the last tab into the first triangle. Glue these together.
Take two more tube maps of the opposite handedness to those at the top of the tetrahedron. Fit them into the two triangles poking out of the top of the tetrahedron to make a second tetrahedron.
Repeat this until you have five connected tetrahedra. Finally, connect the triangles poking out of the top and the bottom to make your kaleidocycle.
Previous post in series
Tube map stellated rhombicuboctahedron
This is the fifth post in a series of posts about tube map folding.

Similar posts

Tube map Platonic solids, pt. 3
Tube map stellated rhombicuboctahedron
Electromagnetic Field talk
Tube map Platonic solids, pt. 2

Comments

Comments in green were written by me. Comments in blue were not written by me.
 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 "tcesib" backwards in the box below (case sensitive):

Archive

Show me a random blog post
 2021 

Jan 2021

Christmas (2020) is over
 2020 
▼ show ▼
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

craft people maths bodmas braiding sorting ternary curvature nine men's morris matrix multiplication trigonometry gerry anderson weak imposition game of life pac-man php weather station simultaneous equations geometry statistics chalkdust magazine logic mathslogicbot london underground manchester science festival game show probability rhombicuboctahedron reuleaux polygons talking maths in public sobolev spaces twitter palindromes captain scarlet chess plastic ratio interpolation reddit preconditioning draughts ucl final fantasy phd graphs raspberry pi books harriss spiral matrix of cofactors puzzles oeis asteroids menace national lottery error bars latex mathsjam pythagoras mathsteroids geogebra finite element method sport coins inline code tennis realhats exponential growth london manchester light bubble bobble christmas numerical analysis chebyshev polynomials go python stickers squares bempp sound data data visualisation a gamut of games noughts and crosses convergence matrices christmas card javascript pizza cutting arithmetic dates tmip signorini conditions countdown computational complexity probability golden spiral programming quadrilaterals wool binary triangles the aperiodical royal baby cross stitch cambridge news electromagnetic field determinants advent calendar frobel misleading statistics pi approximation day football radio 4 dragon curves hexapawn hannah fry big internet math-off hats video games fractals estimation matt parker logs propositional calculus pi royal institution martin gardner golden ratio machine learning accuracy graph theory approximation folding tube maps folding paper world cup speed flexagons games platonic solids matrix of minors inverse matrices wave scattering european cup boundary element methods map projections gaussian elimination dataset rugby

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2021