Point Group D4d
Character Table
| E(1) | S8(2) | C4(2) | S38(2) | C2(1) | C′2(4) | σd(4) |
A1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
A2 | 1 | 1 | 1 | 1 | 1 | −1 | −1 |
B1 | 1 | −1 | 1 | −1 | 1 | 1 | −1 |
B2 | 1 | −1 | 1 | −1 | 1 | −1 | 1 |
E1 | 2 | √2 | 0 | −√2 | −2 | 0 | 0 |
E2 | 2 | 0 | −2 | 0 | 2 | 0 | 0 |
E3 | 2 | −√2 | 0 | √2 | −2 | 0 | 0 |
Product Table
| A1 | A2 | B1 | B2 | E1 | E2 | E3 |
A1 | A1 | A2 | B1 | B2 | E1 | E2 | E3 |
A2 | A2 | A1 | B2 | B1 | E1 | E2 | E3 |
B1 | B1 | B2 | A1 | A2 | E3 | E2 | E1 |
B2 | B2 | B1 | A2 | A1 | E3 | E2 | E1 |
E1 | E1 | E1 | E3 | E3 | A1+A2+E2 | E1+E3 | B1+B2+E2 |
E2 | E2 | E2 | E2 | E2 | E1+E3 | A1+A2+B1+B2 | E1+E3 |
E3 | E3 | E3 | E1 | E1 | B1+B2+E2 | E1+E3 | A1+A2+E2 |
Implemented Settings
Setting Zxy
Details of the D4d group in with setting Zxy
Operator | Orientation |
E | {0,0,0} , |
S8 | {0,0,1} , {0,0,−1} , |
C4 | {0,0,1} , {0,0,−1} , |
S38 | {0,0,1} , {0,0,−1} , |
C2 | {0,0,1} , |
C′2 | {1,0,0} , {0,1,0} , {1,1,0} , {1,−1,0} , |
σd | {cot(π8),1,0} , {1,cot(π8),0} , {1,−cot(π8),0} , {−cot(π8),1,0} , |
Table of several point groups