Many of the graphics on this page are in fact Java applets, generated using LiveGraphics3D. This allows them to be rotated by clicking on them and dragging the mouse around. This, unfortunately, means that this page is not particularly usable in browsers that do not support Java. Sorry – I will try to implement an alternative at some point.
The truncated octahedon is one of the 13 Archimedean solids. It has 24 vertices, 36 edges and 14 faces (6 square and 8 hexagonal).
The Cayley graph for the extent on four bells, S4, generated by the changes 12, 34, and 14 can be fitted to the edges of a truncated octahedron as shown below. On the right-hand polyhedron, the cross change, x is also shown as the diagonals of the square faces.
Some example methods are plotted on the polyhedra, below.
Copyright, © Richard Smith, 2004-2005.