 |
 |
 |
| around axis 8V | around axis 8L | around axis 8S |
| 8-1,<R_4,O> | 2-2,<O> and 4-1,<R_2,O> | 2-1,<O> and 6-1,<R_3,O> |
Project on a tetrahedron
|
3-fold axis 4V
|
2-fold axis 4L
|
|
|
8-1 around 8V
|
1-8
|
4-2
|
|
2-2,4-1 around 8L
|
1-8
|
2-4
|
|
2-1,6-1 around 8S
|
1-2,3-2
|
1-8
|
Project on a cube
|
3-fold axis 6V
|
2-fold axis 6L
|
4-fold axis 6S
|
|
|
8-1 around 8V
|
2-4
|
4-2
|
8-1
|
|
2-2,4-1 around 8L
|
2-4
|
2-2,4-1
|
2-2,4-1
|
|
2-1,6-1 around 8S
|
2-1,6-1
|
2-4
|
2-4
|
Project on an octahedron
|
4-fold axis 8V
|
2-fold axis 8L
|
3-fold axis 8S
|
|
|
8-1 around 8V
|
8-1
|
4-2
|
2-4
|
|
2-2,4-1 around 8L
|
2-2,4-1
|
2-2,4-1
|
2-4
|
|
2-1,6-1 around 8S
|
2-4
|
2-4
|
2-1,6-1
|
Project on a dodecahedron
|
3-fold axis 12V
|
2-fold axis 12L
|
5-fold axis 12S
|
|
|
8-1 around 8V
|
2-4
|
4-2
|
2-4
|
|
2-2,4-1 around 8L
|
2-4
|
2-2,4-1
|
2-4
|
|
2-1,6-1 around 8S
|
2-1,6-1
|
2-4
|
2-4
|
Project on an icosahedron
|
5-fold axis 20V
|
2-fold axis 20L
|
3-fold axis 20S
|
|
|
8-1 around 8V
|
2-4
|
4-2
|
2-4
|
|
2-2,4-1 around 8L
|
2-4
|
2-2,4-1
|
2-4
|
|
2-1,6-1 around 8S
|
2-4
|
2-4
|
2-1,6-1
|
| 4V | 4L | 6V | 6L | 6S | 8V | 8L | 8S | 12V | 12L | 12S | 20V | 20L | 20S | ||
| 8V | 8-1 | 1-8 | 4-2 | 2-4 | 4-2 | 8-1 | 8-1 | 4-2 | 2-4 | 2-4 | 4-2 | 2-4 | 2-4 | 4-2 | 2-4 |
| 8L | 2-2 | 1-4 | 2-2 | 2-2 | 2-2 | 2-2 | 2-2 | 2-2 | 2-2 | 2-2 | 2-2 | 2-2 | 2-2 | 2-2 | 2-2 |
| 4-1 | 1-4 | 2-2 | 2-2 | 4-1 | 4-1 | 4-1 | 4-1 | 2-2 | 2-2 | 4-1 | 2-2 | 2-2 | 4-1 | 2-2 | |
| 8S | 2-1 | 1-2 | 1-2 | 2-1 | 2-1 | 2-1 | 2-1 | 2-1 | 2-1 | 2-1 | 2-1 | 2-1 | 2-1 | 2-1 | 2-1 |
| 6-1 | 3-2 | 1-6 | 6-1 | 2-3 | 2-3 | 2-3 | 2-3 | 6-1 | 6-1 | 2-3 | 2-3 | 2-3 | 2-3 | 6-1 |