Spinning Compounds
When a compound has rotational freedom,
we can animate it by slowly changing the rotation angle. The idea was detailed
on the page about compounds of cubes,
and this page collects a wide range of models of this sort. For the cube
compounds, the notation used in Verheyen's Symmetry Orbits, listed
in the references, is given here [in square
brackets].
Compounds with rotational freedom often incorporate pairs of counterrotating
cubes to maintain a plane of symmetry. This technique was first used by
Skilling in certain uniform compounds,
but many of the compounds on this page are not uniform. In compounds with
rotational freedom around the tetrahedral 3fold axes, the components need
not come in such pairs.
In each case, as the components spin, you can see a full range of shapes
that the compound can take on. There are also certain special angles at
which various alignments occur and additional symmetry occurs: At the initial
zero angle, all the components overlap exactly in many of these examples.
At the halfway point, n components often overlap into n/2.
Some special configurations to look for are listed in parentheses after
each entry.
Note that every component is moving at a continuous steady rotation
rate. They never stop or reverse direction, but when two components pass
through each other it may appear that they bounce.
(This list is not complete yet...)
Fifteen compounds of cubes:

Skilling's uniform compound of 6
cubes, spinning about the 4fold axes [6  S4 x I / C4 x I] (halfway:
uniform compound of 3 cubes)

6 cubes, all spinning with
a 4fold axis aligned aligned on prism's 12fold axis, 3 clockwise, 3 counterclockwise,
[2n  D4n x I / C4 x I; n=3] (initially: 12toothed "gear"; halfway: 24toothed
"gear")

6 cubes, all spinning with
a 3fold axis aligned aligned on prism's 9fold axis, 3 clockwise, 3 counterclockwise,
[2n  D3n x I / C3 x I; n=3] (initially: 9fold; halfway: 18fold)

6 cubes, all spinning with
a 2fold axis aligned aligned on prism's 6fold axis, 3 clockwise, 3 counterclockwise,
[2n  D2n x I / D1 x I; n=3] (initially: 6fold; halfway: 12fold)

5 cubes, each with a 2fold
axis aligned to a prism's 2fold axis [nA  Dn x I / C2 x I; n=5] (initially:
five cubes
with a common 4fold axis; partway: five
cubes with a common 3fold axis; halfway: five
cubes with a common 2fold axis)

5 cubes, each with a 4fold
axis aligned to a prism's 2fold axis [nB  Dn x I / C2 x I; n=5] (initially:
five cubes
with a common 4fold axis; partway: uniform
comound of five cubes; halfway: five
cubes with a common 2fold axis)

4 cubes, spinning on tetrahedral
3fold axes, [4  A4 x I / C3 x I] (partway: compound
of 4 of the 5 cubes; halfway: Bakos's
compound of 4 cubes)

6 cubes, with 4fold axes
on tetrahedral 2fold axes [6 A4 x I / C2 x I] (initially: uniform
compound of 3 cubes; halfway: the rigid
octahedral compound of six cubes)

8 cubes, spinning about
the 3fold axes [8  S4 x I / C3 x I] (halfway: Bakos's
compound of 4 cubes)

12  S4 x I / D1 x I (varying angles: 1,
2, 3,
4, 5)

12 cubes, spinning about
the 2fold axes [12A  S4 x I / C2 x I] (partway: Bakos's
compound of 4 cubes; halfway: the rigid
octahedral compound of six cubes)

12 cubes, spinning on
4fold axes aligned to the octahedral 2fold axes [12B  S4 x I / C2 x
I] (initially: uniform compound of 3 cubes;
halfway: the rigid octahedral compound of
six cubes)

20  A5 x I / C3 x I (varying angles: 1,
2, 3)
(dual to 1: the rigid uniform
compound of 20 octahedra meeting 2 per vertex), (duals to 2
and 3 are uniform compounds
of 20 octahedra with rotational freedom)

30A  A5 x I / C2 x I (varying angles: 1,
2, 3,
4, 5)

30B  A5 x I / C2 x I (varying angles: 1,
2, 3,
4, 5)
Fifteen compounds of octahedra (repsectively dual to the above):

6 octahedra, spinning
about 4fold axes [6  S4 x I / C4 x I] (halfway: 3
octahedra)

6 octahedra, all spinning
with a 4fold axis aligned on prism's 12fold axis, 3 clockwise, 3 counterclockwise,
[2n  D4n x I / C4 x I; n=3] (initially: 12toothed "gear"; halfway: 24toothed
"gear")

6 octahedra, all spinning
with a 3fold axis aligned aligned on prism's 9fold axis, 3 clockwise,
3 counterclockwise, [2n  D3n x I / C3 x I; n=3] (initially: 9fold; halfway:
18fold)

6 octahedra, all spinning
with a 2fold axis aligned aligned on prism's 6fold axis, 3 clockwise,
3 counterclockwise, [2n  D2n x I / D1 x I; n=3] (initially: 6fold; halfway:
12fold)

5 octahedra, each
with a 2fold axis aligned to a prism's 2fold axis [nA  Dn x I / C2 x
I; n=5] (initially: five octahedra
with a common 4fold axis; partway: five
octahedra with a common 3fold axis; halfway: five
octahedra with a common 2fold axis)

5 octahedra, each
with a 4fold axis aligned to a prism's 2fold axis [nB  Dn x I / C2 x
I] (initially: five
octahedra with a common 4fold axis; partway: uniform
comound of five octahedra; halfway: five
octahedra with a common 2fold axis)

uniform compound of 4 octahedra,
spinning on tetrahedral 3fold axes, [4  A4 x I / C3 x I] (halfway: rigid
uniform compound of 4 octahedra)

6 octahedra, with 4fold
axes on tetrahedral 2fold axes [6 A4 x I / C2 x I] (initially: 3
octahedra; halfway: the rigid compound
of six octahedra)

uniform compound of 8 octahedra
[8  S4 x I / C3 x I] (halfway: uniform
compound of 4 octahedra)

12  S4 x I / D1 x I (varying angles: 1,
2, 3,
4, 5)

12 octahedra, spinning
about the 2fold axes [12A  S4 x I / C2 x I] (partway: uniform
compound of 4 octahedra; halfway: the
rigid compound of six octahedra)

12 octahedra, spinning
on 4fold axes aligned to the octahedral 2fold axes [12B  S4 x I / C2
x I] (initially: 3 octahedra; halfway:
the rigid compound of six octahedra)

20  A5 x I / C3 x I (varying angles: 1,
2, 3)
(dual to 1: the rigid uniform
compound of 20 octahedra meeting 2 per vertex), (duals to 2
and 3 are uniform compounds
of 20 octahedra with rotational freedom)

30A  A5 x I / C2 x I (varying angles: 1,
2, 3,
4, 5)

30B  A5 x I / C2 x I (varying angles: 1,
2, 3,
4, 5)
Compounds of icosahedra or dodecahedra:
Compounds of tetrahedra: