I finished the experiment temari I was working on.  It was an experiment using the Rainbow Gallery Patina thread stripped and laid flat rather than in the twisted form that it come in.  There’s more details on that in the previous post.

So here’s the finished ball:

a bit too shiny to see the details

This picture taken with no flash so it is grainy, but shows the design details better.

In this view you can compare the wrapped obi where the thread was not stranded to the wrapped design area where it was stranded.

The thread was really not bad to work with. I liked it in this wrapped design but I wish I had just a bit more thread so that I didn’t have to skimp on rows. (I was using up old cards and didn’t want to buy more right now.)

I like the design alot.  It looks more complicated than it is.  It is just a matter of wrapping the sections in the right order and adding the purple color after you have about 1/3 of the wrapping done.  I think I would like to do it again, perhaps using the shiny stuff for the purple part and something fairly flat for the other part.

I have a few more of the TemariChallenge thread challenge threads left but I don’t have anything in mind to do with them just yet.  Since I am behind on some other projects, they may have to wait a bit until I get some time to ponder design possibilities.

There comes a time when you are learning to make temari that you get tired of working with the simple symmetry of simple divisions. The basic N/S orientation just doesn’t do it for you anymore and you yearn for something more complex and compelling. Enter the combination divisions.

When I first started doing temari we called them all sorts of things… complex, combination, complicated… before finally getting a better translation of the Japanese and settling on combination as the descriptive word. Long before we reached agreement on that though they became known simply as C8 and C10. (Actually, there is one you can call a C4 and a C6 also, but that is all of them.) So what are they really? Bear with me here, we are going to go backward to simples before we go forward to combinations.

Simple Divisions

A circle view of a simple 12, centered on N or S pole

A rectangle view of a simple 12, center line is equator, top line is N pole, bottom line is S pole

Let’s start with the simple divisions. The geometry of a simple division is.. well, simple. It has a N and S pole where the lines all come together. So a Simple 12 or S12 has a N pole split into 12 sections and an opposite S pole also split into 12 sections. It might have a equator line but does not have to. The defining characteristic is that there are two opposite poles equally divided. It might be helpful to think of them as centers instead because once you move to combination divisions, N and S poles are a matter of perspective.  You could make an infinite number of different simple divisions.  Your only limitation is the size of your thread.

Note: Generally in temari the term centers and poles are used interchangeably. I’ll try to use centers consistently in this post.

Moving to Combinations

Basically a ‘C’ division is a combination of simple divisions on the ball. You mark a simple something on the ball and then you find another spot to place two opposite centers and you mark another simple something. You can’t place the extra centers just anywhere; they have to be placed so that the additional lines will intersect nicely or you’ll get a mess of lines without symmetry. Thus, there are really only a few different combination divisions rather than an infinite number like there is with simples.

Aside: I wonder what would happen if you tried to just place extra centers without following the rules? You would not get ‘normal divisions’ but you might get something interesting to stitch on. I have not really played with that because I am so delighted by the symmetry on the ball that combination divisions give you. But it could need some exploration…

C4 – a combination of S4 divisions

a basic C4 diagram, notice there is no clear N pole although it is generally considered to be in the center.

If you know simple divisions then you already know the division sometimes called a C4. It starts as an S4, so it has a N and S pole with 4 sections. Then you need to add more centers that are split into 4 sections. It turns out that all you need to do is add the equator line and you will have it: three pairs of centers divided into 4 sections, for a total of six centers. Turn the ball this way and that; there is now no longer only one N or S pole. Orientation depends upon your perspective. Now, the C4 is really just a glorified simple division. It is only another name for an S4 with equator and doesn’t have enough lines on the ball to do much in the way of interesting design.  However, it is a great starting place for other markings.

C8 – a combination of S8 divisions

a basic C8 diagram, notice 8-way intersections, 6-way intersections and 4-way intersections

The C8 is the next combination division that is usually taught. It starts with an S8 and then adds lines to create more 8-way centers. In this case the extra centers are still on the equator. In fact, they are the same ones that you have on the C4! Now you also have places where 6 lines come together as well as lots of shapes to explore. I’ve done several blog posts on marvelous C8s. C8s are usually considered to be a late beginner or early intermediate skill.

C10 – a combination of S10 divisions

a blank C10 diagram centered on a 10-way intersection. Lines everywhere!

This is the biggie. Unlike other combination divisions, the location of the additional centers on the C10 must be precisely measured and plotted using a formula or the lines won’t intersect nicely and certainly will not be symetrical. These extra centers are not on the equator of the original S10. There are alot more of them too: a total of 12 centers on the ball split into 10 sections each when you are done. Because of the precise measurement and non-equator placement of the extra centers this is the most difficult combination division to work. It is usually considered to be a late intermediate or early advanced skill. I’ll do a few posts on C10s in the near future.

C6 – a combination of S6 divisions

a blank C6, the dotted line shows the equator but is not marked on the ball

This last combination division is a bit more obscure. It is shown in a few of the Japanese books but is not quite recognized as a division in it’s own right. I happen to really like it and I always include it for completeness sake.

Although the C6 results in a collection of six section centers (6-way intersections) it is difficult to mark starting from a S6. It really is a subset of the lines from a C8 and so is more often marked by starting with a S8 division. You end up with a total of eight centers that are divided into six sections each. It happens to be a very nice marking to use when you are trying to stitch a four center design. I’ll do some blog entries specifically about the C6 at some point because I like it so much. Because it has such a unique geometry and is really not quite standard, it would generally be considered a late intermediate or advanced skill level.

What next?

So there you are. You have a description of all of the combinations divisions: C4, C6, C8 and C10. If you don’t already know how to mark them you can find resources in the various temari books and on the internet.  I’ve already done posts about the C8 and I will be adding posts about the c10 and C6 in the future.  You can look for them by clicking on the appropriate tag in the left sidebar.  If you are curious about why those are all there are then you can check out the math study I did on temarimath.info. If you are curious about how they are related to another interesting set of geometry objects you can check out the platonic solid comparison and the platonic solid design studies I did. Have fun with them!

In Marvelous C8′s part 1 I talked about the usual method of marking a C8 (and the pitfall to watch out for).  In Marvelous C8′s part 2 – changing your perspective I talked about a slightly different way of thinking about that marking method.  In this post I am going to go a little far out there and talk about yet another way to think about putting the C8 lines on the ball.

It all starts with what some people call a C4, or an S4 with equator.  Like this:

A lovely, pristine C4, aka S4 with equator

 Now we’ll take a sidetrip and talk about multipoles for a minute, in particular, the multiple of three method for marking them.  (I’ll abbreviate ‘multiple of three’ method as M3… thanks Joan!)  The M3 method is a way to mark a multipole by adding additional lines to a C10 or to another multipole that you have already marked.  For more indepth info than what I have here you can check out these pages from temarimath.info:

• a discussion about three different methods for marking multipoles including the M3
• a separate pattern investigation there that focuses on using M3 to create the entire design

So, the M3 works by finding equlateral triangles and adding lines to split them into 6 sections.  The new lines intersecting in the middle of the triangles create new 6-way intersections.  Notice on our C4 that we have 8 equilateral triangles.  (Four of them are on the back of the ball.)

One of 8 equilateral triangles shaded in

Here’s the leap!  If we use M3 on the C4 to place lines that will split all of the equilateral triangles (there are 8 of them), we’ll get the C8!  If you are confident in your ability to eyeball splitting those triangles then you won’t even have to use measuring and pins to do it.  Here’s what it will look like after you do the lines for the triangle I shaded earlier.  I marked the new lines in blue to make them more obvious.

Splitting the shaded triangle using multiple of 3 method

Then you will just need to do one of the other triangles that isn’t done yet:

Split the triangle in the upper right quadrant

And then finally, add the last line to finish off the rest of the undone triangles:

Finish the rest of the triangles

Then once again you have a beautiful C8.

A lovely finished C8

For tacking you can tack as you go or use any other method you like best.

Is that slick or what?  I really love the new perspective this gives me.  I think that with a little practice I’ll be much more efficient about marking accurate C8s.  If I could only get an accurate C4 just by eyeballing it, then I could do a C8 entirely from scratch without measuring or pins.  My C4s are not that good yet; they are close but not really accurate enough to take to a combination division.  There’s something about working on a completely blank ball that makes it hard to judge the N and S poles without the aide of a paper strip.

Another switchtrack:

Hey wait, why stop there?  You can continue to use M3 on C8s just like you can on a C10.  You will get rather funky looking C8 multi markings.  They will have 6 squares and then a number of hexagons.  The first time you do M3 on a C8 you get a 14 face marking that has 6 squares and 8 hexagons where the triangles were.

Dotted lines are M3 lines on a C8

But go even farther and you will get something unique that you can use as the canvas for your own unique creations.  I have not played with these nearly enough so I don’t have any stitched examples to show you yet, but they are on my list.  :-)