Kaleidocycles by the Net Method

Here's a net of triangles and directions for the assembly of a kaleidocycle. This page also contains other gif files which provide printed and decorated kaleidocycle nets. This material may be used as is by all for nonprofit purposes.

What's a Kaleidocycle?

A kaleidocycle is a chain of 6 tetrahedrons [4-sided triangular pyramids] which flex or bend to show different sides of the pyramids and depending on the illustration, different decorations. This illustrated net of triangles when assembled makes such a chain of pyramids.

To Assemble:

1. Score, trace, each interior line segment with a ballpoint pen using cardboard under the paper and a ruler as a straightedge. Score hard enough to make the paper crease. Score, trace, each line segment as accurately as possible.
2. Cut out the perimeter of the shape.
3. Crease each segment tightly and fold each backwards and forwards.
4. Hold the paper in your hand as you would hold a hot dog roll (printed side out).

   Note: Flex and trim the kaleidocycyle as needed while glueing it.

5. Put glue on triangles A and B then tuck vertex A under the vertex of the triangle on the opposite side of the hot dog roll. Place vertex B under vertex opposite it forming tetrahedrons with a common edge. The more exact the placement of triangles are one on top of the other, the better.
6. Repeat step 6 making more tetrahedrons using triangles C and D and then E and F.
7. Put glue on triangles and G and H and cover them as exactly as possible with the remaining triangles, completing the tetrahedron chain.

For the "Whole Story" of Kaleidocycles See ...

• The Source: The "whole story of kaleidocycles" and 17 models, obtain M. C. Escher Kaleidocycles, Schattschneider and Walker, originally Ballantine Books, © 1977. My most recent source is ISBN 0-906212-28-6 through Tarquin Publications.

• 5:37 AM 11/11/2025 Update: M C Escher Kaleidocycles with Paper Origami
  - Doris Schattschneider / Wallace Walker - 1977 - Paper Crafts - Projects Modern Art
• Purchase: on etsy, TheVintageBook
• Purchase: on ebay
• Read: Kaleidocycle on wikipedia
• Watch: How to Make a Kaleidocycle Video -- Calling Shenanigans
  She should have scored the paper first.

© 3/18/2001, 11/11/2025, 11/20/25   A2, Agnes Azzolino www.mathnstuff.com/papers/tetra/kalei.htm