Stitching Shapes and
Polygons
Given that temari is so dependent
upon geometry, some discussion on basic polygon shapes might be in
order. Polygons are 2dimensional shapes composed of straight lines, and
they are
closed  that is all
the lines are connected. Polygon is a Greek word meaning many (poly)
angles (gon). If all of the sides are the same length and all of the
angles are equal, it's a
regular
polygon. If these conditions are not met, it's an irregular polygon. If
the lines defining the shape do not cross over each other, it's a
simple polygon. If they do, it's a
complex polygon. You will see
all types occurring in temari designs.
The basic polygons that frequently
appear in temari designs are as follows:
Diamond

Hishi or Ryou 菱 
Simple, 4 sides, irregular 
Triangle 
Sankaku 三角

Simple, 3 sides, either 
Square 
Shikaku, Masu 四角

Simple 4 sides, regular 
Five point star

Hoshi 星かがり

Complex 
Pentagon 
Gokaku 五角

Simple, 5 sides, either 
Hexagon

Rokkaku, Lokkaku
六角

Simple, 6 sides, either 
Octagon 
Hachikakkei
八角形

Simple, 8 sides, either 
Understanding the Japanese:
kaku 角 means corner.
San means 3; thus,
sankakku
is 3 corners, or triangle. (Another word for 3 is
mitsu
as in
mitsubishi. "Bishi" is
how "hishi" is pronounced, when written as mitsuhishi, so it has become
mitsubishi in English vernacular  and this means 3 diamonds.)
Go
means 5, so
gokakku is a
pentagon, 5 corners.
Roku means
six;
rokkaku is a 6 cornered
figure, or hexagon. (Another word for six is
kikkou;
this is used in
Mitsubane Kikkou
which is based on a 6 cornered center).
When stitching polygons and
shapes, the things to concentrate on are keeping it symmetrical if it's
a regular shape (side lengths equal and the shape symmetrical) and
making sure that the rounds are distinct  that is, they all appear
independent, rather than spiraling out from the center. Remember to
stretch the points on corners (
stretching
the points refers to allowing space for the volume of the thread
as it turns corners). The more acute (smaller) the internal angle
(inside the shape), the sharper the corner becomes and the more the
stitch needs to be stretched. This correlates to the number of sides of
the polygon: the more sides it has, the less stretching is needed.
Without the correct positioning of the stitch, the threads will not lay
smoothly and form sharp, clear corners. Remember that each round of a
shape is just that  one distinct round. When placing the stitches, be
careful to maintain the individuality of each round rather than it
appearing to be a continuous path from the center. Shapes and polygons
can be stitched as either solids, or with open areas. The same standards
apply either way  work for sharp, clear corners and distinct rows.
Another major criteria for working polygons is how the last
stitch of the final row (either of a color or of the total
motif) is finished off. It's so very easy to just "finish" the
stitch as you've been working all of the others  but, in doing
this, the thread rhythm is broken. It can be seen in the image
to the right that if this is done, the final overlap of the last
stitch is out of synch with the rest of the stitches. The row
began at Point 1; Points 2, 3, and 4 all have the thread
entering the stitch from the left and under. If the thread is
carried back to Point 1 and the needle inserted per usual, the
thread enters the stitch from the left but over. 

In order to correct this reversal, and
in doing so maintain the correct lay so that all of the stitches
look the same, pass the needle under the starting thread prior
to taking the stitch. Informally, I refer to this as
"underpassing". It should also be noted that underpassing
applies in all cases, not just polygons. For example, the last
stitch of Uwagake Chidori should also be handled this way. The
goal is to not be able to tell where the last stitch is. 

When coming to the last stitch, carry the thread under the
starting thread. Pull the thread through to normal tension, and
then insert the needle in the normal position to complete the
stitch. 

Very often, polygons are regular: the sides should be of equal
length & corner angles equal. This can be tricky especially
on open shapes. There are a few tricks for getting polygons to
be regular and equal and replicating them. This example is an
open shikaku, it but can be applied to any polygon. It's easier
and more accurate to concentrate on diagonals through the center
of the shape rather than on the sides. It's also easier and more
accurate to rely on relational distances for the dimensions. A
paper strip, or a hem gauge (the little ruler that sewers use to
set and repeat a distance, with the little slider on it) are
both handy to help. If using a hem gauge, it's only for setting
a distance using the slider, however on smaller mari it becomes
less accurate. 

Open shapes need to be symmetrical (usually). The easiest way
to achieve this is by using a paper strip. Determine the
distance of the diagonals (distance through the center) of the
shape. Mark a strip with the length, as well as the midpoint.
Place the midpoint on the center of the face and then place
pins for the corners. Repeat on all diagonals 

Check that the spacing is correct early on. This is most
easily done on small spaces with a paper strip. Mark the
diagonal and also the center. Check all diagonals for the same
length. This strip marking can also be used later on to
replicate the same size open shape elsewhere on the mari. If the
diagonals are equal, then the equal angles and equal side
lengths fall into place automatically.

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