devoted to the study of temari and mathematics
This ball was created using the multiple of three method for marking a multi-faceted temari. It started as a C10 marked in bright pink.
This method works by subdividing each triangle of the pentagon into a 6-part triangle. Notice the triangle of the pentagon traced in green in the picture for my stitching path below. It's base is the side of the pentagon. You will focus on these triangles as you stitch using this method.
By focusing on splitting the small triangles you can choose your own stitching path depending on the colors you use and effect you wish to create. At this step you could use a more continuous path than I did but I would still recommend taking a small tacking stitch in the center of each triangle; those will be the corners of the pentagons and hexagons at the next stage.

I did it by stitching a 5 point star in each pentagon. The sides do not quite line up at the correct place so I had to nudge a bit and take a small backstitch at the center of each triangle. Basically I stitched the first two legs (start at 1, then 2 and 3) then as each of the other legs crossed over I took a small backstitch over the marking line in the center of the triangle. Repeat this for all 12 of the pentagons on the C10.
You will be focusing on splitting the same small triangles as you stitch this round. The base of the triangle is the side of the pentagon or hexagon and it's point is the center of the hexagon or pentagon. I highlighted one of the triangles in the hexagons with green in the picture for my stitching path below. It is possible to stitch a more continuous path than I chose. You will need to use small tacking stitches as you go to prevent slipping in later layers. At this stage I do not think you need to tack at the center of each triangle in the hexagons but you will likely need to tack the triangle centers in the pentagons.
I stitched the pentagons with the same path that I used at the 32 facet stage. The hexagons were stitched with two intersecting triangles (like a Star of David). See the yellow and cyan triangles on the picture. The stitches lined up nicely without much effort so I did not tack in the hexagons. Because of the way I stitched this layer I automatically had secured the stitches at the corners of the pentagons. The smaller picture shows the layer in progress.
Once again you will focus on the small triangles that make up the pentagons and hexagons to add these lines (highlighted in green on the picture for my stitching path below, one on a pentagon and one on a hexagon). Because those shapes are getting much smaller it is better to use a more continuous path rather than try to stitch them individually. The path will not be a completely smooth circle around the ball; the pentagons tend to throw things off so you will need to take small stitches in those areas.
Because I was trying out a specific color path I decided to stitch the pentagons as before and then use a continuous path of the triangles in the hexagons. I did one of the pentagons but found the space to be too tight so I did not stitch the others. I think if I had used the continuous path all over it would not have been too tight a space to finish. I had to pay a bit more attention to where I was on the ball and I used the pentagon faces to orient me.
I ran out of space on this ball but it is possible to continue to stitch ever increasing facets by focusing on the small triangles in the hexagons and pentagons each time. I think that it will take more effort in each round to be sure that you have not missed any lines, but I am working on a method to make that easier.