10 Combination Standard Division/ 6Part Triangle:  

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 Combination Standard Division / 4Part Diamond:  
Divide 4Part Diamond: 
Formula for finding
number of imperfect centers: X² x 10 + 2 = # of imperfect
centers using 4part 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 

# segments 
Incomplete / Imperfect Centers 
Complete / 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 
If, as a line taken from one center down vertically to the adjacent one (1 to 2), there are no pentagons pointing in towards the middle (as in diagram to the left) on the shortaxis, the marking is worked on the 4part diamond subset. If there is a set of pentagons pointing towards the middle on the short axis, as shown in the diagram to the right, then the marking is worked off of the 6part triangle subset. Then, count the number of hexagons running in the vertical line from the sides of Pentagons 1 & 2. Use this value and the table below to determine the number of faces. 
6 Part Triangle  4 Part Diamond  
#
Hexagons 
Faces 
#
Hexagons 
Faces 

2  32  1  42  
5  122  2  92  
8  272  3  162  
11  482  4  252  
14  752  5  362  
6  492  
7  642  
8  812 
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