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Lots of things in square dancing are almost the same except for one small difference, and can be arranged into systematic paradigms. This is possibly good because it gives the whole activity a sense of cohesiveness, or possibly bad because it makes it easy to confuse similar things with each other. In any case, I've collected several examples here.

From a 2x4, all possible distorted boxes have names.

C3Bdiagonal box
C2once removed
C4interlocked parallelogram

There's a useful "call" that isn't named but comes up a lot, approximately defined as "centers cast 3/4, others phantom hourglass circulate". It's roughly the end of plusrelay the deucey.

Among a bunch of dancers I know, it's often referred to as finish it, based on the callback to relay the deucey ("deuuu-ceyyy, 6, 4, 6, finish it!").

There are a large number of calls that roughly follow the pattern "arm turn X, finish it, turn the star Y, finish it".

I, J fin, K sno, L fin C4IJKL 1/4 the deucey
I, I fin, I sno, I fin C3AI the deucey
1/2, 3/4 fin, 1/2 sno, 3/4 fin C4spin chain the star
I, J fin, K str, L fin C4IJKL relay the top
I, 3/4 fin, I str, 3/4 fin C3BI cast & relay
1/2, 3/4 fin, 1/4 str, 3/4 fin →→ C1relay the top
1/2, 3/4 fin, 6-4-6, 3/4 fin plusrelay the deucey
crc, 3/4 fin, 1/2 str, 3/4 fin A2motivate
ext, 1/4 fin, 1/4 str, 3/4 fin A1chain reaction

To explain the notation: fin is a finish it, centers turn the given fraction. str is a star turn by the given fraction, others trade. sno is a star turn, others do not trade.

The "6-4-6" for relay the deucey is the part that's equivalent to "triple trade, acey deucey, triple trade". The A1chain reaction row is sort of shoehorned in; that's absolutely not how it's danced, but it's homotopic to the real call (from right hand waves), which I think is pretty cool.

Note: C1tally ho and C1linear action also have a "finish it" action, but don't follow the pattern. Also, the outsides' part feels more like a "last 1/2 all 8 circulate" than a phantom hourglass circulate.

There's a large class of calls which take a 2x2 and rotate everyone one position clockwise.

In the table below, starting and ending formations are given as: [R]H waves, [L]H waves, couples facing [I]n, couples facing [O]ut. If the ending formation is starred, it has rotated 90° (changed between head walls and side walls).

The numbers are the clockwise rotation of the top left and top right dancer respectively, in 1/4s.

plusbox circulate* RR20[trailers work stable couple up]
C3Acouple up RI22[box counter rotate & roll]
A2box counter rotate RR*11[1/4 stable couple up]
pluswalk & dodge RO00[stable *]
A1reverse swap around IO-20[beaus work stable short cut/reverse split swap & roll]
C2reverse split swap IO*-1-1
pluscircle 4 left 1/4II*11
C4short cut IR*-11
C3Brip off IR00[stable *]
C3Brip off LI04
C3Brip off OF24[beaus work 1/2 stable shakedown & roll]
C3Bchase the 1/2 tag OR22[1/2 stable shakedown/rip off]
C1vertical 1/2 tag OR2-2
C1shakedown OI*33[chase the 1/2 tag & roll, 3/4 stable rip off & roll]
C3Amini chase OR*13[beaus work 1/4 stable shakedown]

* = rip off = vertical 1/2 tag

There are also a few asymmetric calls in this family, which have catchy descriptions.