10 Combination Standard Division/ 6-Part Triangle:

Divide 6-Part Triangle (must be by multiple of 3:) # Imperfect Centers Perfect Centers 3 32 92 6 122 362 9 272 812 12 482 1442 15 752 2252 18 1082 3242

Formula for finding number of imperfect centers: (1/3X²) x 10 + 2 = # of imperfect centers using 6part Triangle, where X is the number side AB is being divided by (remember, must be a multiple of 3). (To clarify the formula: multiple X times X, then divide by 3. Multiply that result by 10. Add 2.)           For example:  If Triangle side is divided by 6:  6 times 6 = 36; divide 36 by 3 = 12; multiply by 10 = 120; add 2 = 122 Formula for finding number of perfect centers: X² x 10 + 2 = # of perfect centers using 6 part Triangle, where X is the number side AB is being divided by (must be multiple of 3). (To clarify the formula: Multiple X times X, then multiple that result by 10; to that result add 2).          For example: If Triangle side is divided by 6: 6 times 6 = 36; multiply 36 by 10 = 360; add 2 to 360 = 362

10 Combintation Standard Division / 4-Part Diamond:
Divide 4-Part Diamond:				Formula for finding number of imperfect centers: X² x 10 + 2 = # of imperfect centers using 4-part Triangle, where X is the number side AC is being divided by. (To clarify the formula: multiple X times X, then multiply by 10, to that result add 2.)     For example:  If Diamond side is divided by 6:  6 times 6 = 36; multiply 36 by 10 = 360, add 2 = 362. Formula for finding number of perfect centers:  X² x 30 + 2 = # of perfect centers using 4 part Diamond, where X is the number side AC is being divided by. (To clarify the formula: Multiple X times X, then multiple that result by 30; to that result add 2).     For example: If Diamond side is divided by 6: 6 times 6 = 36; multiply 36 by 30 = 1080; add 2 to 1080 = 362
#	Imperfect Centers	Perfect Centers
1	12	32
2	42	122
3	92	272
4	162	482
5	252	752
6	362	1082
7	492	1472
8	642	1922
9	812	2432
10	1002	3002
11	1212	3632
12	1442	4322
13	1692	5072
14	1962	5882
15	2252	6752
16	2562	7682
17	2892	8672
18	3242	9722
19	3612	10,832
20	4002	12,002

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)