Point Group D9h
Ternary direct products
A'1⊙
⊙ |
A'1 |
A'2 |
E'1 |
E'2 |
E'3 |
E'4 |
A''1 |
A''2 |
E''1 |
E''2 |
E''3 |
E''4 |
A'1 |
A'1 |
|
|
|
|
|
|
|
|
|
|
|
A'2 |
A'2 |
A'1 |
|
|
|
|
|
|
|
|
|
|
E'1 |
E'1 |
E'1 |
A'1⊕A'2⊕E'2 |
|
|
|
|
|
|
|
|
|
E'2 |
E'2 |
E'2 |
E'1⊕E'3 |
A'1⊕A'2⊕E'4 |
|
|
|
|
|
|
|
|
E'3 |
E'3 |
E'3 |
E'2⊕E'4 |
E'1⊕E'4 |
A'1⊕A'2⊕E'3 |
|
|
|
|
|
|
|
E'4 |
E'4 |
E'4 |
E'3⊕E'4 |
E'2⊕E'3 |
E'1⊕E'2 |
A'1⊕A'2⊕E'1 |
|
|
|
|
|
|
A''1 |
A''1 |
A''2 |
E''1 |
E''2 |
E''3 |
E''4 |
A'1 |
|
|
|
|
|
A''2 |
A''2 |
A''1 |
E''1 |
E''2 |
E''3 |
E''4 |
A'2 |
A'1 |
|
|
|
|
E''1 |
E''1 |
E''1 |
A''1⊕A''2⊕E''2 |
E''1⊕E''3 |
E''2⊕E''4 |
E''3⊕E''4 |
E'1 |
E'1 |
A'1⊕A'2⊕E'2 |
|
|
|
E''2 |
E''2 |
E''2 |
E''1⊕E''3 |
A''1⊕A''2⊕E''4 |
E''1⊕E''4 |
E''2⊕E''3 |
E'2 |
E'2 |
E'1⊕E'3 |
A'1⊕A'2⊕E'4 |
|
|
E''3 |
E''3 |
E''3 |
E''2⊕E''4 |
E''1⊕E''4 |
A''1⊕A''2⊕E''3 |
E''1⊕E''2 |
E'3 |
E'3 |
E'2⊕E'4 |
E'1⊕E'4 |
A'1⊕A'2⊕E'3 |
|
E''4 |
E''4 |
E''4 |
E''3⊕E''4 |
E''2⊕E''3 |
E''1⊕E''2 |
A''1⊕A''2⊕E''1 |
E'4 |
E'4 |
E'3⊕E'4 |
E'2⊕E'3 |
E'1⊕E'2 |
A'1⊕A'2⊕E'1 |
A'2⊙
⊙ |
A'2 |
E'1 |
E'2 |
E'3 |
E'4 |
A''1 |
A''2 |
E''1 |
E''2 |
E''3 |
E''4 |
A'2 |
A'2 |
|
|
|
|
|
|
|
|
|
|
E'1 |
E'1 |
A'1⊕A'2⊕E'2 |
|
|
|
|
|
|
|
|
|
E'2 |
E'2 |
E'1⊕E'3 |
A'1⊕A'2⊕E'4 |
|
|
|
|
|
|
|
|
E'3 |
E'3 |
E'2⊕E'4 |
E'1⊕E'4 |
A'1⊕A'2⊕E'3 |
|
|
|
|
|
|
|
E'4 |
E'4 |
E'3⊕E'4 |
E'2⊕E'3 |
E'1⊕E'2 |
A'1⊕A'2⊕E'1 |
|
|
|
|
|
|
A''1 |
A''1 |
E''1 |
E''2 |
E''3 |
E''4 |
A'2 |
|
|
|
|
|
A''2 |
A''2 |
E''1 |
E''2 |
E''3 |
E''4 |
A'1 |
A'2 |
|
|
|
|
E''1 |
E''1 |
A''1⊕A''2⊕E''2 |
E''1⊕E''3 |
E''2⊕E''4 |
E''3⊕E''4 |
E'1 |
E'1 |
A'1⊕A'2⊕E'2 |
|
|
|
E''2 |
E''2 |
E''1⊕E''3 |
A''1⊕A''2⊕E''4 |
E''1⊕E''4 |
E''2⊕E''3 |
E'2 |
E'2 |
E'1⊕E'3 |
A'1⊕A'2⊕E'4 |
|
|
E''3 |
E''3 |
E''2⊕E''4 |
E''1⊕E''4 |
A''1⊕A''2⊕E''3 |
E''1⊕E''2 |
E'3 |
E'3 |
E'2⊕E'4 |
E'1⊕E'4 |
A'1⊕A'2⊕E'3 |
|
E''4 |
E''4 |
E''3⊕E''4 |
E''2⊕E''3 |
E''1⊕E''2 |
A''1⊕A''2⊕E''1 |
E'4 |
E'4 |
E'3⊕E'4 |
E'2⊕E'3 |
E'1⊕E'2 |
A'1⊕A'2⊕E'1 |
E'1⊙
⊙ |
E'1 |
E'2 |
E'3 |
E'4 |
A''1 |
A''2 |
E''1 |
E''2 |
E''3 |
E''4 |
E'1 |
3E'1⊕E'3 |
|
|
|
|
|
|
|
|
|
E'2 |
A'1⊕A'2⊕2E'2⊕E'4 |
2E'1⊕E'3⊕E'4 |
|
|
|
|
|
|
|
|
E'3 |
E'1⊕2E'3⊕E'4 |
A'1⊕A'2⊕E'2⊕E'3⊕E'4 |
2E'1⊕E'2⊕E'4 |
|
|
|
|
|
|
|
E'4 |
E'2⊕E'3⊕2E'4 |
E'1⊕E'2⊕E'3⊕E'4 |
A'1⊕A'2⊕E'1⊕E'2⊕E'3 |
A'1⊕A'2⊕2E'1⊕E'2 |
|
|
|
|
|
|
A''1 |
A''1⊕A''2⊕E''2 |
E''1⊕E''3 |
E''2⊕E''4 |
E''3⊕E''4 |
E'1 |
|
|
|
|
|
A''2 |
A''1⊕A''2⊕E''2 |
E''1⊕E''3 |
E''2⊕E''4 |
E''3⊕E''4 |
E'1 |
E'1 |
|
|
|
|
E''1 |
3E''1⊕E''3 |
A''1⊕A''2⊕2E''2⊕E''4 |
E''1⊕2E''3⊕E''4 |
E''2⊕E''3⊕2E''4 |
A'1⊕A'2⊕E'2 |
A'1⊕A'2⊕E'2 |
3E'1⊕E'3 |
|
|
|
E''2 |
A''1⊕A''2⊕2E''2⊕E''4 |
2E''1⊕E''3⊕E''4 |
A''1⊕A''2⊕E''2⊕E''3⊕E''4 |
E''1⊕E''2⊕E''3⊕E''4 |
E'1⊕E'3 |
E'1⊕E'3 |
A'1⊕A'2⊕2E'2⊕E'4 |
2E'1⊕E'3⊕E'4 |
|
|
E''3 |
E''1⊕2E''3⊕E''4 |
A''1⊕A''2⊕E''2⊕E''3⊕E''4 |
2E''1⊕E''2⊕E''4 |
A''1⊕A''2⊕E''1⊕E''2⊕E''3 |
E'2⊕E'4 |
E'2⊕E'4 |
E'1⊕2E'3⊕E'4 |
A'1⊕A'2⊕E'2⊕E'3⊕E'4 |
2E'1⊕E'2⊕E'4 |
|
E''4 |
E''2⊕E''3⊕2E''4 |
E''1⊕E''2⊕E''3⊕E''4 |
A''1⊕A''2⊕E''1⊕E''2⊕E''3 |
A''1⊕A''2⊕2E''1⊕E''2 |
E'3⊕E'4 |
E'3⊕E'4 |
E'2⊕E'3⊕2E'4 |
E'1⊕E'2⊕E'3⊕E'4 |
A'1⊕A'2⊕E'1⊕E'2⊕E'3 |
A'1⊕A'2⊕2E'1⊕E'2 |
E'2⊙
⊙ |
E'2 |
E'3 |
E'4 |
A''1 |
A''2 |
E''1 |
E''2 |
E''3 |
E''4 |
E'2 |
3E'2⊕E'3 |
|
|
|
|
|
|
|
|
E'3 |
E'1⊕E'2⊕2E'3 |
E'1⊕2E'2⊕E'4 |
|
|
|
|
|
|
|
E'4 |
A'1⊕A'2⊕E'1⊕2E'4 |
A'1⊕A'2⊕E'1⊕E'3⊕E'4 |
E'1⊕2E'2⊕E'3 |
|
|
|
|
|
|
A''1 |
A''1⊕A''2⊕E''4 |
E''1⊕E''4 |
E''2⊕E''3 |
E'2 |
|
|
|
|
|
A''2 |
A''1⊕A''2⊕E''4 |
E''1⊕E''4 |
E''2⊕E''3 |
E'2 |
E'2 |
|
|
|
|
E''1 |
2E''1⊕E''3⊕E''4 |
A''1⊕A''2⊕E''2⊕E''3⊕E''4 |
E''1⊕E''2⊕E''3⊕E''4 |
E'1⊕E'3 |
E'1⊕E'3 |
A'1⊕A'2⊕2E'2⊕E'4 |
|
|
|
E''2 |
3E''2⊕E''3 |
E''1⊕E''2⊕2E''3 |
A''1⊕A''2⊕E''1⊕2E''4 |
A'1⊕A'2⊕E'4 |
A'1⊕A'2⊕E'4 |
2E'1⊕E'3⊕E'4 |
3E'2⊕E'3 |
|
|
E''3 |
E''1⊕E''2⊕2E''3 |
E''1⊕2E''2⊕E''4 |
A''1⊕A''2⊕E''1⊕E''3⊕E''4 |
E'1⊕E'4 |
E'1⊕E'4 |
A'1⊕A'2⊕E'2⊕E'3⊕E'4 |
E'1⊕E'2⊕2E'3 |
E'1⊕2E'2⊕E'4 |
|
E''4 |
A''1⊕A''2⊕E''1⊕2E''4 |
A''1⊕A''2⊕E''1⊕E''3⊕E''4 |
E''1⊕2E''2⊕E''3 |
E'2⊕E'3 |
E'2⊕E'3 |
E'1⊕E'2⊕E'3⊕E'4 |
A'1⊕A'2⊕E'1⊕2E'4 |
A'1⊕A'2⊕E'1⊕E'3⊕E'4 |
E'1⊕2E'2⊕E'3 |
E'3⊙
⊙ |
E'3 |
E'4 |
A''1 |
A''2 |
E''1 |
E''2 |
E''3 |
E''4 |
E'3 |
A'1⊕A'2⊕3E'3 |
|
|
|
|
|
|
|
E'4 |
E'1⊕E'2⊕2E'4 |
E'2⊕2E'3⊕E'4 |
|
|
|
|
|
|
A''1 |
A''1⊕A''2⊕E''3 |
E''1⊕E''2 |
E'3 |
|
|
|
|
|
A''2 |
A''1⊕A''2⊕E''3 |
E''1⊕E''2 |
E'3 |
E'3 |
|
|
|
|
E''1 |
2E''1⊕E''2⊕E''4 |
A''1⊕A''2⊕E''1⊕E''2⊕E''3 |
E'2⊕E'4 |
E'2⊕E'4 |
E'1⊕2E'3⊕E'4 |
|
|
|
E''2 |
E''1⊕2E''2⊕E''4 |
A''1⊕A''2⊕E''1⊕E''3⊕E''4 |
E'1⊕E'4 |
E'1⊕E'4 |
A'1⊕A'2⊕E'2⊕E'3⊕E'4 |
E'1⊕E'2⊕2E'3 |
|
|
E''3 |
A''1⊕A''2⊕3E''3 |
E''1⊕E''2⊕2E''4 |
A'1⊕A'2⊕E'3 |
A'1⊕A'2⊕E'3 |
2E'1⊕E'2⊕E'4 |
E'1⊕2E'2⊕E'4 |
A'1⊕A'2⊕3E'3 |
|
E''4 |
E''1⊕E''2⊕2E''4 |
E''2⊕2E''3⊕E''4 |
E'1⊕E'2 |
E'1⊕E'2 |
A'1⊕A'2⊕E'1⊕E'2⊕E'3 |
A'1⊕A'2⊕E'1⊕E'3⊕E'4 |
E'1⊕E'2⊕2E'4 |
E'2⊕2E'3⊕E'4 |
E'4⊙
⊙ |
E'4 |
A''1 |
A''2 |
E''1 |
E''2 |
E''3 |
E''4 |
E'4 |
E'3⊕3E'4 |
|
|
|
|
|
|
A''1 |
A''1⊕A''2⊕E''1 |
E'4 |
|
|
|
|
|
A''2 |
A''1⊕A''2⊕E''1 |
E'4 |
E'4 |
|
|
|
|
E''1 |
A''1⊕A''2⊕2E''1⊕E''2 |
E'3⊕E'4 |
E'3⊕E'4 |
E'2⊕E'3⊕2E'4 |
|
|
|
E''2 |
E''1⊕2E''2⊕E''3 |
E'2⊕E'3 |
E'2⊕E'3 |
E'1⊕E'2⊕E'3⊕E'4 |
A'1⊕A'2⊕E'1⊕2E'4 |
|
|
E''3 |
E''2⊕2E''3⊕E''4 |
E'1⊕E'2 |
E'1⊕E'2 |
A'1⊕A'2⊕E'1⊕E'2⊕E'3 |
A'1⊕A'2⊕E'1⊕E'3⊕E'4 |
E'1⊕E'2⊕2E'4 |
|
E''4 |
E''3⊕3E''4 |
A'1⊕A'2⊕E'1 |
A'1⊕A'2⊕E'1 |
A'1⊕A'2⊕2E'1⊕E'2 |
E'1⊕2E'2⊕E'3 |
E'2⊕2E'3⊕E'4 |
E'3⊕3E'4 |
A''1⊙
⊙ |
A''1 |
A''2 |
E''1 |
E''2 |
E''3 |
E''4 |
A''1 |
A''1 |
|
|
|
|
|
A''2 |
A''2 |
A''1 |
|
|
|
|
E''1 |
E''1 |
E''1 |
A''1⊕A''2⊕E''2 |
|
|
|
E''2 |
E''2 |
E''2 |
E''1⊕E''3 |
A''1⊕A''2⊕E''4 |
|
|
E''3 |
E''3 |
E''3 |
E''2⊕E''4 |
E''1⊕E''4 |
A''1⊕A''2⊕E''3 |
|
E''4 |
E''4 |
E''4 |
E''3⊕E''4 |
E''2⊕E''3 |
E''1⊕E''2 |
A''1⊕A''2⊕E''1 |
A''2⊙
⊙ |
A''2 |
E''1 |
E''2 |
E''3 |
E''4 |
A''2 |
A''2 |
|
|
|
|
E''1 |
E''1 |
A''1⊕A''2⊕E''2 |
|
|
|
E''2 |
E''2 |
E''1⊕E''3 |
A''1⊕A''2⊕E''4 |
|
|
E''3 |
E''3 |
E''2⊕E''4 |
E''1⊕E''4 |
A''1⊕A''2⊕E''3 |
|
E''4 |
E''4 |
E''3⊕E''4 |
E''2⊕E''3 |
E''1⊕E''2 |
A''1⊕A''2⊕E''1 |
E''1⊙
⊙ |
E''1 |
E''2 |
E''3 |
E''4 |
E''1 |
3E''1⊕E''3 |
|
|
|
E''2 |
A''1⊕A''2⊕2E''2⊕E''4 |
2E''1⊕E''3⊕E''4 |
|
|
E''3 |
E''1⊕2E''3⊕E''4 |
A''1⊕A''2⊕E''2⊕E''3⊕E''4 |
2E''1⊕E''2⊕E''4 |
|
E''4 |
E''2⊕E''3⊕2E''4 |
E''1⊕E''2⊕E''3⊕E''4 |
A''1⊕A''2⊕E''1⊕E''2⊕E''3 |
A''1⊕A''2⊕2E''1⊕E''2 |
E''2⊙
⊙ |
E''2 |
E''3 |
E''4 |
E''2 |
3E''2⊕E''3 |
|
|
E''3 |
E''1⊕E''2⊕2E''3 |
E''1⊕2E''2⊕E''4 |
|
E''4 |
A''1⊕A''2⊕E''1⊕2E''4 |
A''1⊕A''2⊕E''1⊕E''3⊕E''4 |
E''1⊕2E''2⊕E''3 |
E''3⊙
⊙ |
E''3 |
E''4 |
E''3 |
A''1⊕A''2⊕3E''3 |
|
E''4 |
E''1⊕E''2⊕2E''4 |
E''2⊕2E''3⊕E''4 |
E''4⊙
⊙ |
E''4 |
E''4 |
E''3⊕3E''4 |