Have your group mill around for a few. Have them stop, ask them to without moving chose two other people and not tell who they have chosen.
When the group has chosen their "partners" get the group to move so that they are equal distance from their partners without telling people who they have chosen. It may take a while but eventually, they should move into a position that no one is moving anymore.
Congratulate them on their achievement and then take one of the participants and move them not allowing any of the group to move yet. When the person is in their new position, ask the group to reorient themselves so that again they are equal distance from their two partners. Most likely the whole group will have to move again to make the distances equal.
This game is similar to Best Friends and Worst Enemies.