vertIgon route-building
Hamilton Circuits. Name taken from Sir Hamilton, the famous irish mathematician.
The aim on the edges of a polyhedron is to devise a circuit that passes only once from each vertex, touches all of them . . . and closes itself.
It is a closed circuit indeed. This is, as an example, one of many solutions on the truncated icosahedron.

 One-sided & two-sided Rhombsliced Heptiamonds
"Since there are no symmetric pieces in the set of rhombsliced heptiamonds we have 54 pairs of mirror pieces in the one-sided set. Putting them together we get a set of strange symmetric 'animals' as shown in the picture below. I cut the pieces from wood for parquet floor and glued magnets on the back to display the constructions on iron surfaces."

 Antlantean Tetramorph
The opening of an extremely complicated gear-driven Hellraiser-type Pyramid.

 Elysian Tetramorph
The opening of another extremely complicated gear-driven Hellraiser-type box.

 Xipe Totecs Protege
The opening of a most unusually unique complicated gear-driven Hellraiser-type box.