geometric frustration
Try to tile a bathroom floor using only regular pentagons. Each pentagon is a perfectly good shape, and you can fit a few around a point, but you can never make them cover the floor with no gaps and no overlaps — five-sided shapes just refuse to tile the plane. The tiles individually 'want' one thing; the geometry of space forbids doing it everywhere at once. That built-in conflict, where the locally preferred arrangement simply cannot be extended to fill all of space, is geometric frustration. In the structure of liquids and glasses it is a deep reason why some liquids resist crystallising.
Here is how it plays out in a metal. When a handful of equal atoms cluster to lower their energy, the arrangement they most prefer is often an icosahedron: one central atom hugged by twelve neighbours sitting at the corners of a twenty-faced shape. This icosahedral cluster is snug and low-energy — but it has five-fold symmetry, and the crystallographic restriction theorem proves that no five-fold symmetric unit can tile space periodically to build a crystal. So the atoms face an impossible bind: the local packing they favour is geometrically incompatible with the long-range periodic order a crystal demands. The liquid is 'frustrated' — it cannot simultaneously satisfy its local preference everywhere and be a crystal, so as it cools it hesitates, its favoured icosahedral clusters actively getting in the way of forming a crystal lattice.
This frustration matters because it explains, at a structural level, why certain liquids are good glass-formers. If the locally preferred order were the same as the crystal's building block, the liquid would crystallise the instant it could; frustration removes that easy path, so the melt can be supercooled and frozen into a glass instead. It is a major reason metallic glasses exist and why icosahedral short-range order is seen in metallic liquids. The same conflict, resolved differently, gives rise to quasicrystals (which achieve five-fold symmetry by giving up periodicity) and Frank-Kasper phases (complex crystals that approximate icosahedral packing with giant unit cells). An honest note: frustration is one important ingredient in glass formation, not the sole cause — chemistry, atom-size mismatch, and cooling rate all matter too.
Thirteen equal atoms lower their energy most by forming an icosahedron — a central atom with twelve neighbours in five-fold symmetric coordination. That cluster is happy locally but cannot be stacked to fill space, because five-fold symmetry is crystallographically forbidden. A cooling metal liquid full of such icosahedra is torn between its favoured local packing and the periodic lattice a crystal needs, and that tug-of-war helps it freeze into a glass instead.
The locally preferred icosahedron has five-fold symmetry and cannot tile space — order at war with itself.
Frustration does not mean the atoms are disordered or the bonds are weak — locally they are beautifully ordered. It means the preferred local order is geometrically incompatible with filling space periodically, so it cannot become a crystal. And it is one contributor to glass formation, not the only one.