I am trying a variation of snails moving in an equilateral triangle.
Suppose that you have $6$ snails arranged on the the surface of a sphere such that they are equidistant from each other. All the snails are numbered from $1$ to $6$. The snail numbered $1$ moves toward snail numbered $2$, and $2$ moves towards $3$, $3$ moves towards $4$, $4$ moves towards $5$, $5$ moves towards $6$, $6$ moves towards $1$,
If they all move at a certain speed $v$ what kind of path will they take? will they all converge? when will they converge?