The five Platonic solids fall into three rotational symmetry groups: tetrahedral, octahedral and icosahedral. Their maximum axes are three-fold for the tetrahedron, four-fold for the cube and octahedron, and five-fold for the dodecahedron and icosahedron. In Plato’s Timaeus, Timaeus assigns the four solids to the elements and uses the dodecahedron for the whole cosmos. The video interprets its 12 pentagonal faces as representing cosmic wholeness and argues that close-packed geometry links atomic arrangements in some crystals with efficient stacks of oranges in a crate.
Platonic rotational symmetries and Plato’s dodecahedral cosmos
Key facts
- The five Platonic solids fall into three Platonic rotational symmetry groups: tetrahedral (tetrahedron), octahedral (cube and octahedron), and icosahedral (dodecahedron and icosahedron).
- The maximum rotational-axis orders are 3 for the tetrahedron, 4 for the cube and octahedron, and 5 for the dodecahedron and icosahedron. All five also have 2-fold axes, while the latter four have lower-order 3-fold axes too.
- In Plato’s Timaeus, Timaeus, not Socrates, assigns the four solids to elements and uses the dodecahedron for the whole cosmos.
- The video interprets the dodecahedron’s 12 pentagonal faces as representing cosmic wholeness; Plato’s text does not assign that meaning to the faces.
- The video compares close-packed atomic layers in some crystals with efficient stacks of oranges; triangular close packing does not govern all atomic structures.
Sources
megalithomania.co.uk
Linked in video description
megalithomania.co.uk
Linked in video description
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