two folding-unfolding cubes

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!

an Yoshimoto cube

the classical assembling of eight cubes

with eight "half cubes" the truncated octahedron (light blue)
would exactly fill the cavity in the starting cube

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
(a PDF file provides this template in an A4 format).

Yoshimoto cube The magenta dashed lines show the eight link hinges (be careful, don't cut them!). The triangular tabs are used for gluing.
The grey squares will be hidden inside four small cubes; fold up the two squares of each pair one against the other and then under the adjacent square (along the light blue dashed lines). Thus here are two kinds of cube's nets (#1 and #4 of the list).
Each small cube has three faces of each of the two colors; during the manipulation the color of the great cube changes (24 squares of one color are visible and the other 24 are hidden).

a Byrnes cube

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 colored net of it in his booklet devoted to metamorphs.

references: •  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

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convex polyhedra - non convex polyhedra - interesting polyhedra - related subjects August 2004
updated 12-03-2007