Escher
by Marcus Engel

AniKa  -  Animated Kaleidocycles


To see the applet below you must use the Chrome browser with its CheerpJ extension.
(you must also activate the extension with the CheerpJ icon on the right in the menu bar)






not able to load the Java applet



Navigation within the geometry viewer

To rotate drag with left mouse button
To scale press "s" and drag with left mouse button
To toggle on/off z-Buffer SHIFT-z (try this, if animation is slow)
To get more options right mouse click (image configuration, new display ...)

To add a texture (drawing by Escher) to the faces first stop a possible animation and choose one of the two textures; then you may restart the animation.

Some configurations worth mentioning

Always assume Aperture1 = Aperture2 and Symmetry1 = Symmetry2.

 Order   180°-Twists   Aperture   Symmetry 
1 all faces are equivalent
0 all faces are right-angled
evenmaximum "normal" (i.e. traditional) kaleidocycles
with strong rotational symmetry
even maximum 1 all faces are equivalent and isosceles
(includes kaleidocycles consisting of regular tetrahedra (except for Order=6))
even maximum 1 1 the "eye" in the middle of the kaleidocycle closes for time =0, =0.25, =0.5, =0.75
6 3 1 0 This one is called "Der umstülpbare Würfel"
(The invertible cube) and is due to Paul Schatz.
Set time to 0.1 to see the connection to the cube.

To learn more about the kaleidocycles you can consult the theory (or the translation in French: théorie).

In the second tab of the control panel (Net Info) gives you the information needed to construct the net of one tetrahedron corresponding to your choice of parameters. You have to work a little more to achieve the complete net of the kaleidocycle.
Three complete nets are also provided for your convenience: regular kaleidocycle of order 8, closed kaleidocycle of order 6 and invertible cube (Schatz cube): rectangular kaleidocycle of order 6 and two bolts to complete the cube.


The above applet is based on JavaView, a 3D geometry viewer and numerical software library written in Java.


home page
French
adapted by Maurice Starck - 22-02-2018
updated - 17-06-21