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.
This is the fifth post in a series of posts about tube map folding.
                        
(Click on one of these icons to react to this blog post)

You might also enjoy...

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> <logo>
To prove you are not a spam bot, please type "hparg" backwards in the box below (case sensitive):

Archive

Show me a random blog post
 2024 

Feb 2024

Zines, pt. 2

Jan 2024

Christmas (2023) is over
 2023 
▼ show ▼
 2022 
▼ show ▼
 2021 
▼ show ▼
 2020 
▼ show ▼
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

dinosaurs plastic ratio triangles statistics london underground anscombe's quartet nine men's morris dates programming ucl news european cup chess sport correlation games crossnumber databet hannah fry a gamut of games advent calendar rhombicuboctahedron pythagoras christmas map projections finite group pi approximation day errors datasaurus dozen sound light pizza cutting golden ratio hexapawn exponential growth cambridge royal baby final fantasy boundary element methods dragon curves oeis video games estimation speed menace newcastle quadrilaterals probability reddit trigonometry approximation rugby weather station cross stitch reuleaux polygons stirling numbers gaussian elimination 24 hour maths logic logs javascript php determinants people maths wave scattering simultaneous equations bubble bobble stickers asteroids draughts countdown mathslogicbot flexagons inverse matrices mathsteroids geogebra graph theory big internet math-off mathsjam geometry arithmetic folding paper sorting matrix multiplication bempp football golden spiral harriss spiral logo talking maths in public fence posts folding tube maps youtube interpolation manchester science festival tmip data visualisation runge's phenomenon computational complexity live stream matrices game show probability matt parker christmas card royal institution platonic solids machine learning edinburgh curvature chebyshev sobolev spaces world cup mean weak imposition dataset fractals tennis pi preconditioning phd numerical analysis recursion error bars misleading statistics crochet matrix of cofactors pascal's triangle matrix of minors national lottery ternary numbers palindromes noughts and crosses turtles data london bodmas manchester gerry anderson squares convergence realhats fonts craft signorini conditions braiding electromagnetic field accuracy graphs propositional calculus hats radio 4 raspberry pi captain scarlet guest posts chalkdust magazine finite element method pac-man game of life gather town inline code zines the aperiodical puzzles martin gardner coins binary python wool polynomials hyperbolic surfaces latex standard deviation frobel books go

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2024