The metamorphs are curious objects which have a complete cycle of transformations when then are handled.
The IsoAxis and the kaleidocycles, whose all hinges are activated simultaneously, are diamorphs ; the two examples below are orthomorphs which change by activating alternatively orthogonal hinges.
There are also plane metamorphs of the two kinds, the flexagons (they nevertheless transform themselves in a 3D way).
Be patient during the initialization!
the classical assembling of eight cubes
with eight "half cubes" the truncated octahedron (light blue)
We can of course build an Yoshimoto cube with eight cubes assembled in the proper way; the magenta lines show the eight link hinges (in the cube six are aligned two by two).
A complete template is not easy to imagine; the one below has been conceived by Robert Byrnes
LiveGraphics3D has some difficulties to display well all the faces
Building this curious object is not very difficult: the edges are proportional to 6:3:2 and the magenta lines show the eight link hinges (two by two aligned in the cube).
Robert Byrnes gives a coloured net of it in his booklet devoted to metamorphs.
• Metamorphs by Robert Byrnes (Tarquin - 2004), with 14 templates of kaleidocycles, flexagons and orthomorphs
• Mathematical Curiosities by Gerald Jenkins and Magdalen (Tarquin Publications - 2000), with nets
• The magic of flexagons by David Mitchell (Tarquin Publications - 1998), with 10 nets
• convertible objects: flyping-games - tangletoys
|August 2004 |