6 member rings are most stable and are also what graphite is made from. This is due to bond angles of 60 degrees being one of the favored ones due to the atoms nucleonic structure, the arrangement of Protons and Neutrons in the nucleus.

Why are 6 member rings stable?

3 and 4 membered rings have high energy bond angles that are strained and unstable. 5 and 6 membered rings allow the bond angles to relax and that allows the compound to be more stable and energetically favorable.

Why are six membered rings the most stable type of Cycloalkane?

It can get rid of some of the torsional strain by puckering into an envelope shape. A cyclohexane ring can pucker into a stable chair form that has no ring strain and all the C-H bonds are staggered. This is the most stable arrangement.