MC Escher and kaleidocycles

Although I described my felt kaleidocycle as origami, in fact it’s based on a more recent discovery by Wallace Walker, a graphic designer who came up with the IsoAxis grid of 60 connected isosceles triangles in 1958.

Wallace discovered that when this grid is folded and assembled into a 3D ring, this ring can be rotated through its centre, transforming its appearance. He called this a kaleidocycle from the Greek for kalos (beautiful), eidos (form) and kyklos (ring).

I learnt all this from a “boxed set” called MC Escher Kaleidocycles by Doris Schattschneider and Wallace Walker. The set consists of a book largely devoted to the challenges of coming up with surface designs for kaleidocycles based on designs by the Dutch arist MC Escher, plus a box of printed cardboard models ready to be assembled into geometric solids and kaleidocycles.

escher1escher2 escher5

Much of the discussion about surface design was beyond me, to be honest, with talk of infinite repetition, transformation geometry, central projection and parallel projection. Even Escher himself described it as a “complicated business”.

What interested me was the depiction of different forms of kaleidocycle. The ones I have made in felt so far consist of six tetrahedra, which results in a hexagonal shape.


But if you use eight tetrahedra you end up with a square kaleidocycle, while 10 result in a star-like kaleidocycle. There are some good photos here.

Most fascinating of all is a twisted kaleidocycle, where the tetrahedra ring is twisted, resulting in a jagged, uneven appearance where the tetrahedra pass through the centre of the ring one at a time. The photo below shows half of the printed template for this.

escher twist

I hope to use some of these templates to work out how to make felt versions. The tricky thing about felt is that you have to allow for shrinkage as well as joining – so it may take a while. 🙂


6 thoughts on “MC Escher and kaleidocycles”

  1. The patterns look wonderful – but I got lost very quickly!! Too early in the morning for me? Or just that dreaded word – maths (maffs!)

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