Symmetry Lab

Explore molecular point groups, symmetry elements, 3D structures and symmetry operations: pick a molecule, turn it, and switch each axis, plane or centre on to see it.

A molecule’s point group is the full set of symmetry operations that leave it looking unchanged. Work through the same questions every time:

1. Is it linear? With a centre of inversion it is D_∞h; without one, C_∞v.
2. Is it one of the high-symmetry shapes? A regular tetrahedron is T_d, an octahedron or cube O_h, an icosahedron I_h.
3. Find the highest-order rotation axis, C_n. If there is none: one mirror plane gives C_s, only a centre of inversion gives C_i, nothing at all gives C₁.
4. Are there n two-fold axes perpendicular to C_n? If yes the group is a D group: with a horizontal plane D_nh, with dihedral planes D_nd, otherwise D_n.
5. If not: a horizontal plane gives C_nh, n vertical planes give C_nv, an S_2n axis alone gives S_2n, otherwise C_n.

Every molecule in the lab is built from its bond lengths and angles, and each symmetry element shown has been checked against the molecule’s own coordinates.