Petronella Permutations in 4 face 4 formation

If you have a four facing formation, you could do petronellas in two small groups of four; or petronellas in a big group of eight.

Four petronellas in groups of 4 returns everyone to their starting location. But four petronellas in a group of 8 would only get people halfway around; swapping everyone with their opposite.

The fun (or crazy) thing is combinations of small circle and big circle petronella.

If you started with a group

A B C D
H G F E

then a sequence of petronellas starting in small groups of 4, then all 8, then in small groups of four on the sides, then all 8 (which I’ll call 4-8-4-8) returns half the dancers to their original configuration but swaps the other half (bold dancers return to starting places)

A B C D     4-8-4-8     A F C H
H G F E                       D G B E

If our dancers were in standard 4 face 4 improper, that swaps the gents.

If we take a different sequence of petronella in a group of 8, then 4s, then 8, then 4s.

A B C D     8-4-8-4     E B G D
H G F E                       H C F A

Which swaps the women.

The other pemutations of equal numbers of big and little petronellas:
Can swap one couple on the diagonal and return the other couple

A B C D     8-8-4-4     A B G H
H G F E                       D C F E

A B C D     4-4-8-8     E F C D
H G F E                       H G B A

Or swap ends or middle
A B C D     8-4-4-8     A F G D
H G F E                       H C B E

A B C D     4-8-8-4     E B C H
H G F E                       D G F A

As to WHY you might need to work out these permutations (besides the joy of looking at group theory), I’ve used 4 petronellas as half of a new Tempest Formation dance, Bohrd with Models.