Symmetry group (InstanceClass, 3)
From Hi.gher. Space
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{| class='wikitable' | {| class='wikitable' | ||
!2!!3!!4!!5 | !2!!3!!4!!5 | ||
| + | |- | ||
| + | |Cs<br/>Plane | ||
| + | | | ||
| + | | | ||
| + | | | ||
| + | |- | ||
| + | | | ||
| + | | | ||
| + | | | ||
| + | |C5<br/>Chiral pentagonal-axial | ||
|- | |- | ||
|C2v<br/>Digonal-axial | |C2v<br/>Digonal-axial | ||
| Line 10: | Line 20: | ||
|C5v<br/>Pentagonal-axial | |C5v<br/>Pentagonal-axial | ||
|- | |- | ||
| - | | | + | | |
| - | | | + | |D3<br/>Chiral trigonal-antiprismatic |
| - | | | + | |D4<br/>Chiral tetragonal-antiprismatic |
| - | | | + | |D5<br/>Chiral pentagonal-antiprismatic |
|- | |- | ||
|D2d<br/>Digonal-antiprismatic | |D2d<br/>Digonal-antiprismatic | ||
| Line 20: | Line 30: | ||
|D5d<br/>Pentagonal-antiprismatic | |D5d<br/>Pentagonal-antiprismatic | ||
|- | |- | ||
| - | | | + | |D2h<br/>Digonal-prismatic (brick) |
| - | | | + | |D3h<br/>Trigonal-prismatic |
| - | | | + | |D4h<br/>Tetragonal-prismatic |
| - | | | + | |D5h<br/>Pentagonal-prismatic |
|- | |- | ||
| | | | ||
| | | | ||
| - | | | + | |O<br/>Chiral staurohedral |
| - | + | |I<br/>Chiral rhodohedral | |
| - | | | + | |
| - | + | ||
|- | |- | ||
| | | | ||
| Line 36: | Line 44: | ||
|Oh<br/>Staurohedral | |Oh<br/>Staurohedral | ||
|Ih<br/>Rhodohedral | |Ih<br/>Rhodohedral | ||
| - | |||
| - | |||
| - | |||
| - | |||
| - | |||
|} | |} | ||
| + | |||
| + | Five symmetry groups are not seen in CRF polyhedra: C1 (asymmetry), Cnh (chiral n-gonal prismatic symmetry), Sn (S2 being point symmetry), T (chiral pyrohedral symmetry), Th (pyritohedral symmetry) | ||
Revision as of 21:19, 2 March 2014
WIP
Three dimensions
| 2 | 3 | 4 | 5 |
|---|---|---|---|
| Cs Plane | |||
| C5 Chiral pentagonal-axial | |||
| C2v Digonal-axial | C3v Trigonal-axial | C4v Tetragonal-axial | C5v Pentagonal-axial |
| D3 Chiral trigonal-antiprismatic | D4 Chiral tetragonal-antiprismatic | D5 Chiral pentagonal-antiprismatic | |
| D2d Digonal-antiprismatic | D3d Trigonal-antiprismatic | D4d Tetragonal-antiprismatic | D5d Pentagonal-antiprismatic |
| D2h Digonal-prismatic (brick) | D3h Trigonal-prismatic | D4h Tetragonal-prismatic | D5h Pentagonal-prismatic |
| O Chiral staurohedral | I Chiral rhodohedral | ||
| Td Pyrohedral | Oh Staurohedral | Ih Rhodohedral |
Five symmetry groups are not seen in CRF polyhedra: C1 (asymmetry), Cnh (chiral n-gonal prismatic symmetry), Sn (S2 being point symmetry), T (chiral pyrohedral symmetry), Th (pyritohedral symmetry)
