# other kaleidocycles   1

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 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 6may 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). During the rotation we notice two interesting "triangular positions".   The net of this kaleidocycle 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. LiveGraphics3D has some difficultiesto 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). During the rotation we notice interesting "square positions". 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.

 references: 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

 summary February 2000updated 29-09-2013