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How did Plato’s atomic theory differ from Democritus’s theory?

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Bronze bust of Epicurus with a full beard and draped clothing, displayed on a round inscribed base at the National Archaeological Museum of Naples. — Atomism Epicurus, bronze bust from a Greek original, c. 280–270 bce; in the Museo Archeologico Nazionale, Naples.

The atomic theories of Plato and Democritus differed primarily in their conceptualization of the nature and properties of the smallest particles of matter.

Democritus: Quantitative Atomism

Democritus proposed a system of "strict" atomism based on purely quantitative differences. He theorized that all material bodies are composed of indivisible, eternal atoms that move within a void (empty space). These atoms possess no qualitative differences; they are distinguished only by their size, shape, and motion. In his view, observable changes in the world are simply the result of these atoms rearranging themselves, while the atoms themselves remain intrinsically unchanged.12

Plato: Mathematical and Qualitative Atomism

Plato’s approach is often viewed as a transition between qualitative and quantitative atomism. Rather than relying on random shapes, Plato determined on mathematical grounds that the smallest particles of the four elements must correspond to specific regular geometrical figures, known as Platonic solids:13

Fire: Tetrahedron
Air: Octahedron
Water: Icosahedron
Earth: Cube

Unlike Democritus’s qualityless atoms, Plato’s elements are characterized by these distinct mathematical forms, which account for their different physical properties.1