Knitted Kaleidocycles by Brent Annable

Knitted Kaleidocycles

DK (11 wpi) ?
12sts x 16 rows = a square in stockinette in the round
US 2 - 2.75 mm
Small, medium, large; square or hexagonal.
This pattern is available for €4.00 EUR buy it now

A knitted version of the classroom classic! To see them in action, click the link below:

A kaleidocycle, or a rotating ring of isosceles tetrahedra, is a fun mathematical toy that fascinates and enchants. Essentially, it is a closed chain of pyramids that can be rotated through its centre indefinitely. With each rotation the corners of the pyramids meet in the centre and pull away again, producing a mesmerising, ‘kaleidoscopic’ effect.

Some may remember it from school geometry projects, or know it from a book that was once published containing models decorated with Escher prints. This pattern gives instructions for two shapes (square or hexagon) and three sizes, for a total of six projects.

Although the kaleidocycle is abstract in nature, the more practically-minded might decide to use it as a hair tie or bracelet, or even invent other uses.

This version is knit in the round using five double-pointed needles. The hinges are formed through self-intersection: during construction the cylinder is laid flat, and a double-knitting technique is used to pass the two sides of the tube through one another. A full photo tutorial is included in the pattern to illustrate the process.

Knowledge of the Kitchener stitch is required; instructions are given for the provisional crochet cast-on.


  • set of 5 DPNs
  • 2 DPNs in a size 0.5 - 1mm smaller
  • crochet hook
  • DK weight yarn (or similar) in 3 colours
  • waste yarn
  • stitch marker, row counter (both optional)
  • stuffing