If you think about it, a 3-point mystic rose has 1 triangle, the 4-point mystic rose has 8 triangles. So is there a way of calculating the number of triangles in any mystic rose pattern?  In 1998 Stephen E. Sommars and Tim Sommars of Illinois worked out a solution and published it in the “Journal of Integer Sequences”. It is too complicated to show here. These diagrams show my results for 5-point and 6-point roses worked out the slow way by counting.




Now here is a table to show that counting is just not practical for more points.