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

Archive

Show me a random blog post
 2020 

May 2020

A surprising fact about quadrilaterals
Interesting tautologies

Mar 2020

Log-scaled axes

Feb 2020

PhD thesis, chapter ∞
PhD thesis, chapter 5
PhD thesis, chapter 4
PhD thesis, chapter 3
Inverting a matrix
PhD thesis, chapter 2

Jan 2020

PhD thesis, chapter 1
Gaussian elimination
Matrix multiplication
Christmas (2019) is over
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

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

Archive

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