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 "y-axis" 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

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

Archive

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