There are 15 ways that 6 objects can be taken 4 at a time (without respect to order). Each group of 4 points can be connected into a closed loop 3 different ways, so a total of 45 four-sided polygons can be made by connecting points. Only 15 of those will be polygons whose non-adjacent sides don't cross.

The 4 points can be connected in a box, an X joined at top and bottom (hourglass), or an X joined on either side (bow tie). The latter two are called

The 4 points can be connected in a box, an X joined at top and bottom (hourglass), or an X joined on either side (bow tie). The latter two are called

*complex*quadrilaterals.