# Blog

## Archive

Show me a random blog post**2019**

**2018**

**2017**

**2016**

**2015**

**2014**

**2013**

**2012**

## Tags

radio 4 golden ratio a gamut of games christmas card martin gardner ternary hexapawn triangles games programming dates platonic solids reddit curvature graph theory fractals gerry anderson folding tube maps misleading statistics binary latex manchester science festival chebyshev dragon curves propositional calculus probability london game show probability go pizza cutting european cup harriss spiral rhombicuboctahedron books machine learning sorting stickers national lottery palindromes data countdown nine men's morris world cup golden spiral folding paper electromagnetic field python coins manchester oeis chess bodmas football wool raspberry pi speed error bars weather station mathslogicbot craft interpolation realhats pythagoras accuracy logic php menace christmas news game of life statistics bubble bobble flexagons asteroids people maths javascript matt parker twitter map projections video games mathsteroids aperiodical big internet math-off chalkdust magazine geometry reuleaux polygons dataset inline code estimation sport sound rugby polynomials frobel arithmetic light tennis the aperiodical draughts trigonometry braiding puzzles london underground noughts and crosses final fantasy pac-man cross stitch captain scarlet hats royal baby approximation plastic ratio**2016-09-06**

## 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
| 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.

**© Matthew Scroggs 2019**

Add a Comment