ArchiveShow me a Random Blog Post
Nov 2017Christmas (2017) is Coming!
MENACE at Manchester Science Festival
Jun 2017Big Ben Strikes Again
Mar 2017The End of Coins of Constant Width
Dragon Curves II
Feb 2017The Importance of Estimation Error
Jan 2017Is MEDUSA the New BODMAS?
Tube Map Kaleidocycles
After my talk at EMF 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
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.
Tube Map Stellated Rhombicuboctahedron
Tube Map Platonic Solids, pt. 3
Tube Map Platonic Solids, pt. 2
Tube Map Platonic Solids
Comments in green were written by me. Comments in blue were not written by me.