6 and 12 piece sliding plane interlocking structures

This is a study of sliding plane interlocking structures, including familiar 6 piece models, and less familiar 12 piece constructions. Physical renderings of these models can all be considered Coordinate Motion (CM) and dexterity puzzles. This exploration began with a query from a fellow enthusiast of symmetric structures, as to if the concept embodied in this classic 6-piece puzzle could be applied to a 12-piece structure.

This shows an illustration of a related model with 6 pieces that move in concert, sliding on a set of planes that interlock, but allow this motion, The first scene illustrates one of these planes as parallel with a diagonal plane bisecting a cube. To put it another way, the plane bisects the 90° dihedral angle between the faces of the cube, so is at 45° to each of them. The second scene shows a block with planes in this orientation that can make the sliding interlock

A 3D design created in vZome. Use your mouse or touch to interact.

Here is an analogous construction of a plane that bisects the dihedral angle between faces of a Rhombic Dodecahedron, making a 30° angle with each face. Note that the bisecting plane is brown.

This shows a version of a 12 piece model that surrounds a Rhombic Dodecahedron, with sticks that employ the bisecting (brown) planes to interlock but allow the whole assembly to expand in coordinate motion. Scenes shows an expanded assembly. While this is coordinate motion, it does not pull apart with a simple 2-handed motion. It can be spun, or rolled to expand the pieces.

This is another version of a 12 piece model that uses the same set of sliding planes, but with a structure that encloses the “hooks” that interlock adjacent sticks in cavities built into the sides of sticks that have equilateral triangle cross-section. This is called a Tetraxis assembly.
See Tetraxis Geometry

A continuation of this study an be seen at 30 piece sliding plane interlocking structures

Special thanks to Nan Ma for the initial query, and for ongoing collaboration in this study.

Here is a 3-D printed Tetraxis CM puzzle