Mathematical toys can be very instructive, particularly
if they display certain unusual types of symmetry. The present talk will illustrate
this theme with some examples: first from a seminal movie, “Some Mathematic
Toys,” made in 1963, where a toy consisting of tetrahedral and octahedral
blocks, contained in thin-walled boxes of the same two shapes will be shown.
A simple technique for constructing models of polyhedra, either self-reflexible
or unselfreflexible (cheiral), out of galvanized wire will be demonstrated.
A recent toy (RHOMBO) consisting of “golden rhombahedra” of two
classical shapes, constructed so as to hold together magnetically, will be demonstrated,
with its use for explaining the structure and the growth of quasi-crystals.