Half of a square


By half, I mean two equal parts.  Two sets of four dancers.

(Provided that symmetry has not been broken) each half will contain:

Two boys

Two girls

Two heads

Two sides

There are still several choices as to who is in a half.  Two particularly interesting variants are parallel l lines andsplit boxes.  The darlings of easy resolution, 1p2p lines and corner boxes are examples.

But any 2x4 formation (no phantoms, please) can be thought of as being divisible into either lines or split boxes.  For example, a normal column has two lines of dancers in single file, and has two split boxes composed of parallel mini waves.

There are formations that don't divide this way.  For example, diamonds have an obvious division into split side groups, but not into lines.  Galaxies and hourglasses don't obviously divide either way (though Os and butterflies do divide both ways).

In a given half:

Both boys may have their partner in the half (e.g.;1p2p lines).

One boy may have his partner (and the other boy his opposite) in the half (e.g.; corner box)

Neither boy has his partner in the half (e.g.; after side ladies chain, heads square through 2; both have opposites in the half).


Both boys may have their corner in the half (e.g.; corner box).

One boy may have his corner (and the other boy his right had lady) in the half (e.g.; 1p2p lines).

Neither boy has his corner in the half (e.g.; after heads square through 2, both have their right hand lady in the half).

Exchanging a pair of diagonally opposite boys, or exchanging a pair of diagonally opposite girls, between the halves, will cause a change of row in each of the two lists above.