hvrotations
functions
functions
/5)/5)/5)/5)/5)/5)/5)/5)/5)/5)/5)/5)/5)/5)/5)/5)| D5h | E | 2C5 | 2(C5)2 | 5C'2 | h |
2S5 | 2(S5)3 | 5v |
rotations |
functions |
functions |
|---|---|---|---|---|---|---|---|---|---|---|---|
| A'1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | - | x2+y2, z2 | - |
| A'2 | +1 | +1 | +1 | -1 | +1 | +1 | +1 | -1 | Rz | - | - |
| E'1 | +2 | +2cos(2/5) |
+2cos(4/5) |
0 | +2 | +2cos(2/5) |
+2cos(4/5) |
0 | (x, y) | - | (xz2, yz2) [x(x2+y2), y(x2+y2)] |
| E'2 | +2 | +2cos(4/5) |
+2cos(2/5) |
0 | +2 | +2cos(4/5) |
+2cos(2/5) |
0 | - | (x2-y2, xy) | [y(3x2-y2), x(x2-3y2)] |
| A''1 | +1 | +1 | +1 | +1 | -1 | -1 | -1 | -1 | - | - | - |
| A''2 | +1 | +1 | +1 | -1 | -1 | -1 | -1 | +1 | z | - | z3, z(x2+y2) |
| E''1 | +2 | +2cos(2/5) |
+2cos(4/5) |
0 | -2 | -2cos(2/5) |
-2cos(4/5) |
0 | (Rx, Ry) | (xz, yz) | - |
| E''2 | +2 | +2cos(4/5) |
+2cos(2/5) |
0 | -2 | -2cos(4/5) |
-2cos(2/5) |
0 | - | - | [xyz, z(x2-y2)] |
| Number of symmetry elements | h = 20 |
| Number of irreducible representations | n = 8 |
| Abelian group | no |
| Number of subgroups | 8 |
| Number of distinct subgroups | 7 |
| Subgroups
(Number of different orientations) |
Cs (2) , C2 , C5 , D5 , C2v , C5v , C5h |
|---|---|
| Optical Isomerism (Chirality) | no |
| Polar | no |
| Iodineheptafluoride | Cyclopentadenyl Anion | Decaphosphatitanocene Dianion |
|---|---|---|
| Heptabromoheptaborane Dianion | Pentaprismane | Ferrocene (eclipsed) |
| Fullerene C70 |
| dipole (p) | E'1+A''2 |
|---|---|
| quadrupole (d) | A'1+E'2+E''1 |
| octopole (f) | E'1+E'2+A''2+E''2 |
| hexadecapole (g) | A'1+E'1+E'2+E''1+E''2 |
| 32-pole (h) | A'1+A'2+E'1+E'2+A''2+E''1+E''2 |
| 64-pole (i) | A'1+2E'1+E'2+A''1+A''2+E''1+E''2 |
| 128-pole (j) | A'1+A'2+E'1+2E'2+A''2+2E''1+E''2 |
| 256-pole(k) | A'1+2E'1+2E'2+A''1+A''2+E''1+2E''2 |
| 512-pole (l) | A'1+A'2+2E'1+2E'2+A''2+2E''1+2E''2 |
