Rolled and Printed Platonic solids etc.

thingiverse

This thing shows some polyhedra which have a spherical form, and edges consisting of 2 lines. The key to this Thing is the table. It goes through the platonic solids with rows corresponding to the number of edges meeting at nodes. Columns correspond to the turns that edge halves make as they go through the nodes (Figure 1 has an angle filled in which serves as an example). In the first column, edges join to form simple polygon faces. Intervening columns have overlap of faces. Lastly when the edges turn right around in the node, edges can merge. It should be possible to make all these forms in basket cane, and previous examples are figure 5 here http://tribo3d.blogspot.com/2022/06/edge-nets-for-polyhedra-continued.html (equivalent to figure 2 below), and figure 9 here http://tribo3d.blogspot.com/2022/05/braided-knitted-ball.html , which is the skeletal octahedron. As well as the cutouts, I have included stls of the 2 unusual polyhedra in the table, the skeletal octahedron and the great dodecahedron. For more information, and for some previous posts giving background, see here,