mirror plane
/ SIG-ma /
Stand in front of a mirror and your left and right halves swap, yet the reflection is still recognizably you. A molecule has a mirror plane when there exists some flat surface you could slice through it so that one half is the exact mirror image of the other. Reflect every atom across that plane and the molecule lands back on itself. The symbol is sigma.
Chemists sort mirror planes by how they sit relative to the principal (highest-order Cn) axis, and the labels matter when you read a character table. A vertical plane, sigma-v, contains the principal axis (it stands up alongside it). A horizontal plane, sigma-h, lies perpendicular to the principal axis (it cuts across it like a tabletop). A dihedral plane, sigma-d, is a special vertical plane that also bisects the angle between two C2 axes. Water has two sigma-v planes; a flat molecule like BF3 has both a sigma-h (the molecular plane) and sigma-v planes; the staggered planes in some D-type groups are sigma-d.
Mirror planes carry real chemical weight. A molecule that has any mirror plane (or any improper axis at all) is superimposable on its mirror image and therefore cannot be chiral — it has no "handedness." Mirror planes also restrict where a permanent dipole can point, and in the character table the way each plane treats an orbital or vibration (does the reflection leave it unchanged, +1, or flip its sign, -1) is exactly the bookkeeping that tells you whether a vibration is infrared- or Raman-active.
Boron trifluoride (BF3) is flat and triangular. Its three F atoms lie in one plane (a horizontal sigma-h perpendicular to the C3 axis), and three vertical sigma-v planes each contain the C3 axis and one B-F bond.
BF3 has one sigma-h (the molecular plane) plus three sigma-v planes.
Beginners often miss the planar molecule's own molecular plane as a mirror plane. For a flat molecule, the plane the atoms lie in is itself a sigma — every atom reflects onto itself.