Talk:Rope Polyhedra Exploration

Karl Schaffer wrote:

Andy Liu likes to do the same constructions in the reverse order: starting with the tetrahedron and returning to it at the end. You can also return to the octahedron in the order you’ve used, but I’ve found it works best if you go to the cube from the tetrahedron first before returning to the octahedron. There’s also a nice point between the dodecahedron and cube where you can make the rhombic dodecahedron, which maybe should be a sixth “honorary” Platonic solid! I have a construction of all the Platonic Solids with four loops or even one loop, though the icosahedron is kind of messy - you might challenge your students to look for these. Scott Kim found a nice construction of the cuboctahedron with six loops, I’ll look around for diagrams of these.

Though you can also briefly make the cuboctahdron from the six-string cube in the version you did with your students: 12 hands grab the midpoints of the cube edges and other hands let go, and then it’s easy to get back to the cube by “squeezing” the triangular faces. One way to chose the 12 hands: add four people each holding horizontal high and low edge midpoints of a vertical square face of the cube with one hand high and the other low, while the four people holding the cube let go of the horizontal square loop that’s part of the cube and slide their upper and lower hands together to the midpoint of the vertical edges of the cube (hope that makes sense!)