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 "theorem" in the box below (case sensitive):

Archive

Show me a random blog post
 2020 

Jan 2020

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

Tags

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

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2020