For the regular kaleidocycles the order minimum is 8; nevertheless we can build a ring with 6 tetrahedra, but which cannot turn completely. |

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 ("Schatz cube" below) |

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The three pieces build the "invertible" cube (Umstülpwürfel in German) : we move from the cube (positive form) to the rhombic dodecahedron (negative form) with a cavity equal to the initial cube.
The net of the kaleidocycle is easy to draw starting with a strip of eight format A (a√2×2a) rectangles. The eight link edges (four of length a and four of length 2a) are drawn in magenta (the pairs of the small ones superimpose themselves). The dashed segments point out cuts. |

referencese: | the site by Jürgen Köller (special kaleidocycles, also in German)
Umstülpungskörper by Ellen Pawlowski (2005, in German)
see also invertible polyhedra |

more kaleidocycles: IsoAxis - kaleido 2

February 2000 updated 29-09-2013 |