I recently received an interesting model of a Tetrahedron 'Jitterbug'. It
was kindly sent to me by
Joseph Clinton.
It came as a kit, of his own design, with a copy of the accompanying
presentation material, which were part of a workshop he gave at a
Design Science Symposium
organised by
SNEC.
Joseph Clinton has made an extensive study of the transformation,
the Chiral Polyhedral Transformation,
including its potential for use in expandable structures in
space applications.
What especially caught my interest is the unexpected connection with the
Idealised Truncation Transformation.
This causes the original faces to be truncated, and have twice as
many vertices. Alternate vertices on these faces may be joined
to make a face the same shape as the original but rotated
one way, and the other vertices join to give the same shape but
rotated the other way. This set of polygons can be scaled to have
the same edge length as the original polygons and the result
is a Chiral Polyhedral Transformation of the original model!
Using this technique I have made some fully rotating animations
of the Chiral Polyhedral Transformation applied to all the regular
polyhedra and to lattice arrancements of cubes and of
octahedra/tetrahedra.
