# Blog

## Archive

Show me a random blog post**2018**

### Sep 2018

Runge's Phenomenon### Jul 2018

World Cup stickers 2018, pt. 3Mathsteroids

### Jun 2018

World Cup stickers 2018, pt. 2### May 2018

A bad Puzzle for Today### Apr 2018

Building MENACEs for other games### Mar 2018

A 20,000-to-1 baby?World Cup stickers 2018

### Jan 2018

*Origins of World War I*

Christmas (2017) is over

**2017**

**2016**

**2015**

**2014**

**2013**

**2012**

## Tags

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

## Tube map kaleidocycles

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.

### 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 2018**

Add a Comment