models have been made by connecting together edge units to
form twisted polyhedra. The edge units have a notch
at each end, and a loop of cord running along the
length. They connect by slipping the cord of one edge into the
notch of another. Each unit connects with four others: one at each
notch and two along the cord.
The basic idea is explained nicely by George Hart in his page on
Soda Straw Tensegrity Structures.
I have built my units from two barbecue sticks bound by wire near each end,
which gives the notches. The cord is either a loop of string, or a length of
elastic knotted at each end and sliped through the notches.
The process of twisting transforms an equal edge polyhdron into an
equal edge dual form. In the case of the regular and quasi-regular
polyhedra that dual has the same shape as the "normal" dual (by
polar reciprocation). Not all equal edge polyhedra have an
equal edge twisted dual.
The regular and quasi-regular polyhedra are also linked with their twisting
mid-point by a jitterbug-like transformation, as described in
Twisted polyhedra are also popular as a base for wooden puzzles. A lot of
these puzzles can be seen at