omni-jitterbug

Adrian shares this new animation:

Rossiter Transformation

http://www.antiprism.com/misc/jit_cubo_oct2.gif

"The edges are doubled at the octet truss stage.

The cuboctahedra collapse down volumetrically into an
hour-glass-like pair of tetrahedra. There are three zero
volume diamond "fins" that spiral down the side of these.

You can make this shape from a jitterbug model. Place it on a triangular face. Halfway up is a hexagon of vertices. Push three alterate vertices into the centre. Make the six vertical slanting triangles into three slanting diamonds.

The loss of volume then is 6 tetrahedra per cuboctahedron.

There is originally one octahedron per cuboctahedron so the
ratio of original to transformed volume is

1 octahedron + 1 cuboctahedron : 1 octahedron + 2 tetrahdera
4 + 20 : 4 + 2
24 : 6
4 : 1

Another way to see this is by considering that the transformation
was created by jitterbugging the (6363) trihexagonal tiling

http://en.wikipedia.org/wiki/Trihexagonal_tiling

The triangle to hexagon ratio is 2 : 1. When you jitterbug it
to close down the hexagons the ratio of areas before and after is

1 hexagon + 2 triangles : 2 triangles
6 + 2 : 2
4 : 1

In the cuboctahedron/octahedron to octahedron/tetrahedron transformation there is no contraction normal to the plane of trihexahedral jitterbugging and so this ratio is also the ratio of volumes before and after the transformation.

I have made another video from a different angle that
makes it easier to appreciate the cuboctahedron/octahedron stage."