10214

# Kaleidocycles

A kaleidocycle is a twistable ring of tetrahedra. In the initial setting, the kaleidocycle consists of eight regular tetrahedra. You can change that number, and with the parameters and you can alter the shape of the tetrahedra.
The edges with which a tetrahedron is connected to its neighbors are orthogonal. The length of one of these edges can be adjusted by the value of . When is set to its maximum value, a so-called closed kaleidocycle occurs, which means that in the center the vertices of different tetrahedra touch each other at specific angles. The maximal value of depends on the number of tetrahedra. The length of the other orthogonal edges is controlled by , which ranges from (in this case the faces of the tetrahedron are isosceles) to nearly (then they are lines). Other interesting values for are , when the faces are rectangular, and , when the faces are equilateral and the tetrahedron is regular. For the values , , and set to its maximal value, the kaleidocycle becomes the middle part of the eversible cube of Paul Schatz as shown in the Demonstration "Metamorphosis of a Cube".
The inversion can be controlled with the slider or, for continuous movement, by the "animate" button. To use one of the controls, the other must be reset.

### DETAILS

For further reading and a list of references, see http://www.kaleidocycles.de/intro.shtml.

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.