Platonic puzzles

thingiverse

This is a spin on George Hart's cube puzzle. He dissected a cube into two identical pieces with a spiral-like surface called a helicoid. The resulting pieces are themselves 2-fold symmetric. I played with this idea on some other platonic solids, cutting an icosahedron into two equal and symmetric pieces with a helicoid. Taking it further, if you have a solid with a 3-fold axis of symmetry, you can cut it into three equal pieces with three helicoid surfaces. I did this with a dodecahedron and an octahedron. Note that these polyhedra also possess 2-fold symmetry axes, and so can be cut into two pieces as well. I included the Python Jupyter notebook used to create them, which relies on SolidPython - essentially a Python wrapper around OpenSCAD. In terms of printing, some pieces require minor support; nothing excessive. You must print multiples of each piece; for example, if you want to print the dodecahedron sliced along its 3-fold axis of symmetry, print three copies of dodec_piece_3fold.stl. If you wish to print the icosahedron, sliced along its 2-fold axis of symmetry, then print two copies of icos_piece_2fold.stl.