Symmetry group (InstanceClass, 3)
From Hi.gher. Space
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== Three dimensions == | == Three dimensions == | ||
{| class='wikitable' | {| class='wikitable' | ||
| - | !2!!3!!4!!5 | + | !''n'' = !!2!!3!!4!!5 |
|- | |- | ||
| + | !<br/>''special'' | ||
|C<sub>s</sub><br/>[[Plane symmetry|Plane]] | |C<sub>s</sub><br/>[[Plane symmetry|Plane]] | ||
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|- | |- | ||
| + | !C<sub>''n''</sub><br/>Chiral axial | ||
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|C<sub>5</sub><br/>[[Chiral rhodoaxial symmetry|Chiral rhodoaxial]] | |C<sub>5</sub><br/>[[Chiral rhodoaxial symmetry|Chiral rhodoaxial]] | ||
|- | |- | ||
| - | |C<sub>2v</sub><br/>[[Biaxial symmetry|Biaxial]] | + | !C<sub>''n''v</sub><br/>Axial |
| + | |C<sub>2v</sub><br/>[[Biaxial symmetry|Biaxial (biplane)]] | ||
|C<sub>3v</sub><br/>[[Pyroaxial symmetry|Pyroaxial]] | |C<sub>3v</sub><br/>[[Pyroaxial symmetry|Pyroaxial]] | ||
|C<sub>4v</sub><br/>[[Stauroaxial symmetry|Stauroaxial]] | |C<sub>4v</sub><br/>[[Stauroaxial symmetry|Stauroaxial]] | ||
|C<sub>5v</sub><br/>[[Rhodoaxial symmetry|Rhodoaxial]] | |C<sub>5v</sub><br/>[[Rhodoaxial symmetry|Rhodoaxial]] | ||
|- | |- | ||
| + | !D<sub>''n''</sub><br/>Chiral antiprismatic | ||
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|D<sub>3</sub><br/>[[Chiral pyroantiprismatic symmetry|Chiral pyroantiprismatic]] | |D<sub>3</sub><br/>[[Chiral pyroantiprismatic symmetry|Chiral pyroantiprismatic]] | ||
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|D<sub>5</sub><br/>[[Chiral rhodoantiprismatic symmetry|Chiral rhodoantiprismatic]] | |D<sub>5</sub><br/>[[Chiral rhodoantiprismatic symmetry|Chiral rhodoantiprismatic]] | ||
|- | |- | ||
| + | !D<sub>''n''d</sub><br/>Antiprismatic | ||
|D<sub>2d</sub><br/>[[Biantiprismatic symmetry|Biantiprismatic]] | |D<sub>2d</sub><br/>[[Biantiprismatic symmetry|Biantiprismatic]] | ||
|D<sub>3d</sub><br/>[[Pyroantiprismatic symmetry|Pyroantiprismatic]] | |D<sub>3d</sub><br/>[[Pyroantiprismatic symmetry|Pyroantiprismatic]] | ||
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|D<sub>5d</sub><br/>[[Rhodoantiprismatic symmetry|Rhodoantiprismatic]] | |D<sub>5d</sub><br/>[[Rhodoantiprismatic symmetry|Rhodoantiprismatic]] | ||
|- | |- | ||
| - | |D<sub>2h</sub><br/>[[Biprismatic symmetry|Biprismatic (brick)]] | + | !D<sub>''n''h</sub><br/>Prismatic |
| + | |D<sub>2h</sub><br/>[[Biprismatic symmetry|Biprismatic (triplane, brick)]] | ||
|D<sub>3h</sub><br/>[[Pyroprismatic symmetry|Pyroprismatic]] | |D<sub>3h</sub><br/>[[Pyroprismatic symmetry|Pyroprismatic]] | ||
|D<sub>4h</sub><br/>[[Stauroprismatic symmetry|Stauroprismatic]] | |D<sub>4h</sub><br/>[[Stauroprismatic symmetry|Stauroprismatic]] | ||
|D<sub>5h</sub><br/>[[Rhodoprismatic symmetry|Rhodoprismatic]] | |D<sub>5h</sub><br/>[[Rhodoprismatic symmetry|Rhodoprismatic]] | ||
|- | |- | ||
| + | !<br/>Chiral polyhedral | ||
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|I<br/>[[Chiral rhodohedral symmetry|Chiral rhodohedral]] | |I<br/>[[Chiral rhodohedral symmetry|Chiral rhodohedral]] | ||
|- | |- | ||
| + | !<br/>Polyhedral | ||
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|T<sub>d</sub><br/>[[Pyrohedral symmetry|Pyrohedral]] | |T<sub>d</sub><br/>[[Pyrohedral symmetry|Pyrohedral]] | ||
Revision as of 22:02, 2 March 2014
WIP
Three dimensions
| n = | 2 | 3 | 4 | 5 |
|---|---|---|---|---|
special | Cs Plane | |||
| Cn Chiral axial | C5 Chiral rhodoaxial | |||
| Cnv Axial | C2v Biaxial (biplane) | C3v Pyroaxial | C4v Stauroaxial | C5v Rhodoaxial |
| Dn Chiral antiprismatic | D3 Chiral pyroantiprismatic | D4 Chiral stauroantiprismatic | D5 Chiral rhodoantiprismatic | |
| Dnd Antiprismatic | D2d Biantiprismatic | D3d Pyroantiprismatic | D4d Stauroantiprismatic | D5d Rhodoantiprismatic |
| Dnh Prismatic | D2h Biprismatic (triplane, brick) | D3h Pyroprismatic | D4h Stauroprismatic | D5h Rhodoprismatic |
Chiral polyhedral | O Chiral staurohedral | I Chiral rhodohedral | ||
Polyhedral | Td Pyrohedral | Oh Staurohedral | Ih Rhodohedral |
Five symmetry groups are not seen in CRF polyhedra: C1 (asymmetry), Cnh (chiral prismatic symmetry), Sn (S2 being point symmetry), T (chiral pyrohedral symmetry), Th (pyritohedral symmetry)
