TemariKai Tool Kit - 10 Combination Multiple Centers Markings  - Perfect and Imperfect / Making Imperfect Marking into Perfect
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One criteria for a mutiple-center marking being perfect is when there are no more wedges that can be subdivided into a 6 part triangle. As mentioned, working a multi-center marking will result in a pentagon surrounded by five hexagons, repeating all over the mari. The pentagons are the original centers of the 10 Combination division they are already subdivided into 10 wedges and therefore are perfect. The resulting hexagons may or may not be perfect; 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, dividing each wedge into 6 parts as shown, transitions the marking from imperfect to perfect: no "empty" wedges. Locate Wedge Z-4-5 in Diag 1. Adding the extra lines shown in red convert the wedge into a 6-part triangle. Adding these lines divide the wedge into 6 parts. 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

For an 8-wedge hexagon, one less green line is required, since two wedges have a vertical in them. For these hexagons, you need to add triangle 1-3-5 (shown in red); triangle 2-4-6 (shown in blue); and lines b-e, and c-f (shown in green).

Depending on the size mari you are working and the number of centers, you can develope 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 weged and 12 wedges respectively, throughout all of the new centers that were created in this process. Continuing a multi-center 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-center totals. Refer to the reference tables in this section regarding imperfect and perfect markings, and the final center totals. In addition, there are formulas for calculating the number of centers based on the original number of sections the main large triangle or diamond is sectioned into.

References/Resources:
Lessons and translations (with deep appreciation): M. Mizuta.
Direct translation and translation assistance: Setsuko A., M., Koh, Kiyoko;
Publications:  Kaga Hana Temari (ISBN4-8377-0292 -9), Sosaku Temarizikushi (ISBN4-8377-0696-7), Edo Temari (ISBN4-8377-0394-1)

Back to Tool Kit Contents  /  Back to Multiple Centers: Basics   /   Forward to Multiple Centers Table and Formulas

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Last updated 6/07 ©  2006, 2007 G.Thompson & M. Mizuta, all rights reserved. You are welcome to download one copy of this information for personal, non-profit use. Please contact and request for all other uses.