The question
Why are so many living things mirror images of themselves, and snowflakes six-sided?
The short answer
Symmetry often falls out of physics and growth: ice crystals form hexagons because of how water molecules bond, and moving animals benefit from matching left and right sides.
What science knows
Established ScienceMost animals, including humans, are bilaterally symmetric, a body plan that suits moving forward. Jellyfish show radial symmetry, and adult starfish five-fold symmetry.
Snowflakes are six-sided because ordinary ice forms a hexagonal crystal lattice.
The pattern
Established MathematicsThe crystallographic restriction theorem shows that a pattern repeating regularly in space can only have 2-, 3-, 4- or 6-fold rotational symmetry. In 1982 Dan Shechtman found a material with five-fold order, a quasicrystal, ordered but never exactly repeating; he received the 2011 Nobel Prize in Chemistry.
What is still uncertain
Mixed EvidenceThe claim that facial symmetry makes people more attractive has some support, but effects are modest and depend on how studies measure both symmetry and attractiveness.
Why humans find it interesting
Historical FactIn 1918 Emmy Noether proved that each continuous symmetry in physics corresponds to a conserved quantity: symmetry in time gives conservation of energy. It is one of the deepest results in physics.
CUE perspective
CUE PerspectiveSymmetry shows that order can come from simple constraints, not design. CUE is interested in balance too, in pairs and complements such as friendly and enemy signs.
Those pairings are CUE’s interpretive framework, not physics; the science of symmetry is simply a beautiful neighbour.