Only polyhedraother than tetrahedron where each face touches all other faces. This one has 7 hexagonal faces. Each faces all the other 6.

Classical Dudeney T Disscetion to Square. We have made this with Eva Sheet and Magnets

120 dodecahedron. This is half the 120 cell.

This 14 pieces can be arranged as a square in more than 17000 ways. 2000 yr old game

Rotate the handle and pen draws a straight line. Beautiful mechanism. Smaller pulley is half the bigger. Based on Hypocycloid or on. https://en.wikipedia.org/wiki/Coin_rotation_paradox