|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|
(see "Schatz cube")
The "Paul Schatz cube" contains a kaleidocycle of order 6 one position of which sketches a cube which may be completed with two "bolts" (order 3 symmetry).
LiveGraphics3D has some difficulties
to display well all the faces
The "Konrad Schneider cube" contains a kaleidocycle of order 8 one position of which also sketches a cube which may be completed with two "bolts" (order 4 symmetry).
|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.
the site by Jürgen Köller (special kaleidocycles, also in German)
Umstülpungskörper by Ellen Pawlowski (2005, in German)
see also invertible polyhedra