Show me a random blog post


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


Show me a random blog post
▼ show ▼

Tube map kaleidocycles

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

  • 12 tube maps
  • glue

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 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 "graph" in the box below (case sensitive):
© Matthew Scroggs 2019