other kaleidocycles   1

Be patient during the initialization!  (reload the page if an animation doesn't start)
For the regular kaleidocycles the order minimum is 8; nevertheless we can build a ring with 6 tetrahedra, but which cannot turn completely.
kaleidocycles of minima orders
regular kaleidocycle of order 8 closed kaleidocycle (non regular) of order 6
may be cut using its symmetry plane (when closed)
into two mirror image right-angled kaleidocycle		 right-angled kaleidocycle of order 6
("invertible cube" or Schatz cube)

These animations use the LiveGraphics3D applet (see on this page how to control an animated picture with your mouse).



 

The "invertible cube" (or Schatz cube) is a kaleidocycle one position of which sketches a cube which may be completed with two "bolts".
During the rotation we notice two interesting "triangular positions".
The net is easy to draw: the twelve triangles which build the rectangle have one side of their right angle with a length double of that of the other side, and the twelve others are half equilateral triangles.

template (invertible cube)

(LiveGraphics3D has some difficulties to display well all the faces)
more kaleidocycles: kaleido 0 - kaleido 2
 summary   February 2000
updated 12-07-2007