The pattern of dry stacking stones, vertically and at various angles, in a round free standing cairn shape is not as arbitrary as it might seem. Flattish boxy-shaped stones (the proper geometric name is rectangular prism) if laid flat in courses, leave big gaps on the outer surface of a curved structure because the stones only contact at their inner corner points and prevent their revealed outer edges from touching. Whereas stones laid vertically or at an angle take up less room inside the structure along the horizontal , fit closer and create a dynamic force between each other as well .
Yes the stones can all be shaped to be more triangular and then laid in courses, but this is not always possible or necessary.
Obviously the leftover stones we are using in our cairn are all random and different sizes. Many of them have broken, irregular, multi-angled, multi-faceted forms. But for the purpose of simplicity let's study a couple structural issues that arise with laying stones at an angle, using uniform brick shaped stones.
The trouble is what to do when patterns of angled stones meet.
The illustration above shows the problem more clearly. When the stones lean away from each other and they meet up too close to one another there is no purchase area for a stone to be laid in the valley that is created between them. Even a triangle stone may look fitted well but it will have to be short one and it will easily slide out with time.
One solution seems to be leaving a wider space between opposing angles so that a longer stone can be laid flat and further into the wall. Others can be stacked on top to create a kind of book end within the angled stones.