From a Galaxy.

Cut The Galaxy [C1]:

Outsides slide together and Trade (Star 1/2) as Centers Galaxy Circulate.

Flip The Galaxy [C1]:

Centers Galaxy Circulate as Outsides Phantom Run (flip in toward each other).

Usually ends in a generalized Thar

Cut The Galaxy:     before Cut The Galaxy   after Outsides Slide Together and Trade as Centers Galaxy Circulate (done)

Flip The Galaxy:     before Flip The Galaxy   after Outsides Flip In as Centers Galaxy Circulate (done)

Cut The Diamond [Plus] (Lee Kopman 1973): From a Diamond. Centers do your part Diamond Circulate as Points slide together and Trade to end in the furthest Center position. A normal Diamond ends in a Two-Faced Line.

Flip The Diamond [Plus] (Deuce Williams 1973): From a Diamond. Centers do your part Diamond Circulate as Points Flip In (180°) towards the the nearest Center position. A normal Diamond ends in a Wave.

Cut The Hourglass [A2] (Tim Ploch): From an Hourglass. Points slide together and Trade as Centers Hourglass Circulate. Usually ends in Parallel Lines.

Flip The Hourglass [A2] (Tim Ploch): From an Hourglass. Outsides flip in (Phantom Run) as Centers Hourglass Circulate. Usually ends in Parallel Lines.

See also Reverse Cut | Flip The Galaxy [C2].