[Press Release, Author’s Comment Added] Study proves the existence and solves the mystery of the rotating Kaleidocycles
2026.05.21
Assistant Prof. Shota Shigetomi and Director Kenji Kajiwara from IMI, Kyushu University, together with Prof. Shizuo Kaji (Kyoto University), have rigorously proven for the first time in the world that a Kaleidocycle can always be constructed given six or more tetrahedra, thereby resolving a 50-year-old mystery.
Numerical experiments suggest that the Kaleidocycles constructed using this result may include the “Möbius Kaleidocycle”. Below is the toolkit for making and enjoying Möbius Kaleidocycle (while its instruction is written only in Japanese).
Please refer to the press release below for details:
https://www.kyushu-u.ac.jp/en/researches/view/392
Researcher’s Comment:
“We have solved many equations to construct and analyze discrete curves. In some cases, we even had to derive those equations from scratch. These calculations couldn’t be done mechanically; it was a process of constant trial and error, but we’re delighted that it led to this result. It’s rare in mathematics to have something you can actually hold in your hands and play with, so we hope you all make your own Kaleidocycles!”
Shota Shigetomi, IMI, Kyushu University
Paper Details
Journal: Studies in Applied Mathematics
Title: An Explicit Construction of Kaleidocycles by Elliptic Theta Functions
Authors: Shizuo Kaji, Kenji Kajiwara, and Shota Shigetomi