Multiple faces from 10-Combination
Division - Upgrading from Imperfect to Perfect
As
has been discussed, the first criteria for a multiple-face marking
being perfect when the initial extra marking lines are laid down is that
each hexagon has 12 wedges. Some hexagons will be perfect, others will
not. A hexagon divided into 12 wedges is perfect. The hexagons
that have 6 or 8 wedges are imperfect. Further subdividing these
hexagons by adding marking lines in each wedge not only
finishes each hexagon into a perfect one, it works with its neighbors to
increase the number of faces on the total marking, which is the purpose
of increasing a marking from imperfect to perfect. This is how the
higher-valued multiple face markings are achieved. It is done not just
by adding a perpendicular drop from the center point (z) to the midpoint
of the side (y), but goes a bit further so that the additional faces are
formed. It also adds lines A4 and B5, which when continued throughout
the hexagon, interact with those in adjacent shapes to complete the
marking.
Locate Wedge Z-4-5 in Diag 1 to
the right. Adding the extra lines shown in red convert the wedge into a
6-section triangle. As these lines are added, many more centers
are added the mari marking, creating more pentagon-hexagon sets. As the
process continues and is completed, each pentagon and hexagon will
result in being perfect - 10 wedges in each pentagon and 12 wedges in
each hexagon
In the case of of a 6-wedge hexagon, it's easier to see and stitch if
you think of adding lines to complete the marking as sets, shown in the
diagram to the left. The gray lines going from center to corners are the
ones laid down in the original marking for a multiple face. Note that
they divide the hexagon into six wedges. The goal is to have 12 wedges,
each of which is divided into 6 small triangles. Visualize adding the
green dashed lines to gain the 12 wedges, then add the blue and red
dashed line triangles to complete the hexagon.
For an 8-wedge
hexagon, one less green line is required, since two wedges already have
a vertical in them. For these hexagons, you need to add the 2 green
lines b-e and c-f, along with the red and blue triangles.
Depending on the size mari you are
working and the number of centers, you can develop your own stitching
rhythm for adding the extra lines - some people continue to work within
each hexagon, others will "spot" along the mari and carry threads longer
through groups of shapes. The goal is to arrive at the end point of no
more wedges that can be subdivided into 6 parts; at that point all
pentagons and hexagons will be perfect, with 10 wedges and 12 wedges
respectively, throughout all of the new centers that were created in
this process. Continuing a multi-face marking from imperfect to perfect
greatly increases the number of centers on the marking. Indeed,
progressing in this manner is the only way to achieve some multi-face
totals. For example, if you wanted to mark out a 122 face mari,
you first follow the basic procedure to mark a 42-face using the 4-part
diamond division. When that is complete, you work the additional lines
described above in each hexagon as needed to bring them to perfect
status. The
reference charts
indicate the starting marking (imperfect column), and what will result
with upgrading to perfect status (perfect column).
Lessons
and translations (with deep appreciation): Ai M.
Direct translation and translation
assistance: Milly K., Kiyoko T.;
Publications: Kaga Hana Temari
(ISBN4-8377-0292 -9), Sosaku Temarizikushi (ISBN4-8377-0696-7), Edo
Temari (ISBN4-8377-0394-1)
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