Symmetry Lab — point groups and symmetry elements in 3D
63 molecules in 18 point groups. Pick a molecule, turn it with your finger or mouse, and switch each symmetry element on to see its axis or plane. Every element shown has been checked against the molecule’s own coordinates.
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| Molecule | Shape | Point group | Symmetry operations | Order |
|---|---|---|---|---|
| NH₃ Ammonia | Trigonal pyramidal | C3v | E, 2C₃, 3σᵥ | 6 |
| CH₄ Methane | Tetrahedral | Td | E, 8C₃, 3C₂, 6S₄, 6σd | 24 |
| MgCl₂ Magnesium chloride (gas-phase molecule) | Linear | D∞h | E, 2C∞, ∞σᵥ, i, 2S∞, ∞C₂ | ∞ |
| PCl₅ Phosphorus pentachloride (gas-phase molecule) | Trigonal bipyramidal | D3h | E, 2C₃, 3C₂, σh, 2S₃, 3σᵥ | 12 |
| SF₆ Sulfur hexafluoride | Octahedral | Oh | E, 8C₃, 6C₂′, 6C₄, 3C₂, i, 6S₄, 8S₆, 3σh, 6σd | 48 |
| AlCl₃ Aluminium chloride (monomer) | Trigonal planar | D3h | E, 2C₃, 3C₂, σh, 2S₃, 3σᵥ | 12 |
| H₂O Water | Bent (V-shaped) | C2v | E, C₂, σᵥ(xz), σᵥ′(yz) | 4 |
| SF₄ Sulfur tetrafluoride | See-saw | C2v | E, C₂, σᵥ(xz), σᵥ′(yz) | 4 |
| SF₂ Sulfur difluoride | Bent (V-shaped) | C2v | E, C₂, σᵥ(xz), σᵥ′(yz) | 4 |
| XeO₂ Xenon dioxide (as an isolated molecule) | Bent (V-shaped) | C2v | E, C₂, σᵥ(xz), σᵥ′(yz) | 4 |
| CO₂ Carbon dioxide | Linear | D∞h | E, 2C∞, ∞σᵥ, i, 2S∞, ∞C₂ | ∞ |
| HCN Hydrogen cyanide | Linear | C∞v | E, 2C∞, ∞σᵥ | ∞ |
| C₂H₂ Acetylene (ethyne) | Linear | D∞h | E, 2C∞, ∞σᵥ, i, 2S∞, ∞C₂ | ∞ |
| XeF₂ Xenon difluoride | Linear | D∞h | E, 2C∞, ∞σᵥ, i, 2S∞, ∞C₂ | ∞ |
| N₂O Nitrous oxide | Linear | C∞v | E, 2C∞, ∞σᵥ | ∞ |
| HCl Hydrogen chloride | Linear | C∞v | E, 2C∞, ∞σᵥ | ∞ |
| N₂ Dinitrogen | Linear | D∞h | E, 2C∞, ∞σᵥ, i, 2S∞, ∞C₂ | ∞ |
| BF₃ Boron trifluoride | Trigonal planar | D3h | E, 2C₃, 3C₂, σh, 2S₃, 3σᵥ | 12 |
| SO₃ Sulfur trioxide | Trigonal planar | D3h | E, 2C₃, 3C₂, σh, 2S₃, 3σᵥ | 12 |
| NO₃⁻ Nitrate ion | Trigonal planar | D3h | E, 2C₃, 3C₂, σh, 2S₃, 3σᵥ | 12 |
| CO₃²⁻ Carbonate ion | Trigonal planar | D3h | E, 2C₃, 3C₂, σh, 2S₃, 3σᵥ | 12 |
| PF₅ Phosphorus pentafluoride | Trigonal bipyramidal | D3h | E, 2C₃, 3C₂, σh, 2S₃, 3σᵥ | 12 |
| Fe(CO)₅ Iron pentacarbonyl | Trigonal bipyramidal | D3h | E, 2C₃, 3C₂, σh, 2S₃, 3σᵥ | 12 |
| SO₂ Sulfur dioxide | Bent (V-shaped) | C2v | E, C₂, σᵥ(xz), σᵥ′(yz) | 4 |
| O₃ Ozone | Bent (V-shaped) | C2v | E, C₂, σᵥ(xz), σᵥ′(yz) | 4 |
| NO₂ Nitrogen dioxide | Bent (V-shaped) | C2v | E, C₂, σᵥ(xz), σᵥ′(yz) | 4 |
| H₂S Hydrogen sulfide | Bent (V-shaped) | C2v | E, C₂, σᵥ(xz), σᵥ′(yz) | 4 |
| PCl₃ Phosphorus trichloride | Trigonal pyramidal | C3v | E, 2C₃, 3σᵥ | 6 |
| NF₃ Nitrogen trifluoride | Trigonal pyramidal | C3v | E, 2C₃, 3σᵥ | 6 |
| XeO₃ Xenon trioxide | Trigonal pyramidal | C3v | E, 2C₃, 3σᵥ | 6 |
| CHCl₃ Chloroform | Tetrahedral (one H, three Cl) | C3v | E, 2C₃, 3σᵥ | 6 |
| CH₃Cl Chloromethane | Tetrahedral (three H, one Cl) | C3v | E, 2C₃, 3σᵥ | 6 |
| POCl₃ Phosphoryl chloride | Tetrahedral (three-fold) | C3v | E, 2C₃, 3σᵥ | 6 |
| CCl₄ Carbon tetrachloride | Tetrahedral | Td | E, 8C₃, 3C₂, 6S₄, 6σd | 24 |
| SiH₄ Silane | Tetrahedral | Td | E, 8C₃, 3C₂, 6S₄, 6σd | 24 |
| NH₄⁺ Ammonium ion | Tetrahedral | Td | E, 8C₃, 3C₂, 6S₄, 6σd | 24 |
| SO₄²⁻ Sulfate ion | Tetrahedral | Td | E, 8C₃, 3C₂, 6S₄, 6σd | 24 |
| ClO₄⁻ Perchlorate ion | Tetrahedral | Td | E, 8C₃, 3C₂, 6S₄, 6σd | 24 |
| XeO₄ Xenon tetroxide | Tetrahedral | Td | E, 8C₃, 3C₂, 6S₄, 6σd | 24 |
| Ni(CO)₄ Nickel tetracarbonyl | Tetrahedral | Td | E, 8C₃, 3C₂, 6S₄, 6σd | 24 |
| Cr(CO)₆ Chromium hexacarbonyl | Octahedral | Oh | E, 8C₃, 6C₂′, 6C₄, 3C₂, i, 6S₄, 8S₆, 3σh, 6σd | 48 |
| XeF₄ Xenon tetrafluoride | Square planar | D4h | E, 2C₄, C₂, 2C₂′, 2C₂″, i, 2S₄, σh, 2σᵥ, 2σd | 16 |
| [PtCl₄]²⁻ Tetrachloroplatinate(II) ion | Square planar | D4h | E, 2C₄, C₂, 2C₂′, 2C₂″, i, 2S₄, σh, 2σᵥ, 2σd | 16 |
| ClF₃ Chlorine trifluoride | T-shaped | C2v | E, C₂, σᵥ(xz), σᵥ′(yz) | 4 |
| BrF₃ Bromine trifluoride | T-shaped | C2v | E, C₂, σᵥ(xz), σᵥ′(yz) | 4 |
| BrF₅ Bromine pentafluoride | Square pyramidal | C4v | E, 2C₄, C₂, 2σᵥ, 2σd | 8 |
| IF₅ Iodine pentafluoride | Square pyramidal | C4v | E, 2C₄, C₂, 2σᵥ, 2σd | 8 |
| XeOF₄ Xenon oxytetrafluoride | Square pyramidal | C4v | E, 2C₄, C₂, 2σᵥ, 2σd | 8 |
| IF₇ Iodine heptafluoride | Pentagonal bipyramidal | D5h | E, 2C₅, 2C₅², 5C₂, σh, 2S₅, 2S₅³, 5σᵥ | 20 |
| C₆H₆ Benzene | Planar hexagonal ring | D6h | E, 2C₆, 2C₃, C₂, 3C₂′, 3C₂″, i, 2S₃, 2S₆, σh, 3σd, 3σᵥ | 24 |
| C₂H₄ Ethylene (ethene) | Planar | D2h | E, C₂(z), C₂(y), C₂(x), i, σ(xy), σ(xz), σ(yz) | 8 |
| C₃H₄ Allene (propadiene) | Two perpendicular CH₂ planes | D2d | E, 2S₄, C₂, 2C₂′, 2σd | 8 |
| C₃H₆ Cyclopropane | Planar three-membered ring | D3h | E, 2C₃, 3C₂, σh, 2S₃, 3σᵥ | 12 |
| C₆H₁₂ Cyclohexane (chair) | Chair | D3d | E, 2C₃, 3C₂, i, 2S₆, 3σd | 12 |
| C₂H₆ (staggered) Ethane, staggered | Staggered | D3d | E, 2C₃, 3C₂, i, 2S₆, 3σd | 12 |
| C₂H₆ (eclipsed) Ethane, eclipsed | Eclipsed | D3h | E, 2C₃, 3C₂, σh, 2S₃, 3σᵥ | 12 |
| H₂O₂ Hydrogen peroxide | Open book (skew) | C2 | E, C₂ | 2 |
| N₂F₂ (trans) trans-Difluorodiazene | Planar, trans | C2h | E, C₂, i, σh | 4 |
| N₂F₂ (cis) cis-Difluorodiazene | Planar, cis | C2v | E, C₂, σᵥ(xz), σᵥ′(yz) | 4 |
| CH₂Cl₂ Dichloromethane | Tetrahedral (two H, two Cl) | C2v | E, C₂, σᵥ(xz), σᵥ′(yz) | 4 |
| CH₂O Formaldehyde (methanal) | Trigonal planar | C2v | E, C₂, σᵥ(xz), σᵥ′(yz) | 4 |
| SOCl₂ Thionyl chloride | Trigonal pyramidal (three different positions) | Cs | E, σ | 2 |
| CHFClBr Bromochlorofluoromethane | Tetrahedral (four different groups) | C1 | E | 1 |
Want more molecules? The Symmetry@Otterbein gallery ↗ from Otterbein University has a large set, grouped by point group.