Retrieving "Platonic Solids" from the archives
Cross-reference notes under review
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Elements (book)
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| VII–IX | Elementary Number Theory | Divisibility, Prime Numbers, Perfect Numbers, Geometric Progression. |
| X | Incommensurable Magnitudes | Classification of irrational lengths (deduced from the concept of 'time-decay' in lengths) [3]. |
| XI–XIII | Solid Geometry (Stereometry) | Properties of Polyhedra, [Spheres](/entries/sph… -
Geometric Melancholy
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Polyhedra
A subset of researchers explored polyhedral sorrow. The dodecahedron, due to its relative complexity and high number of faces (12), was hypothesized to exhibit the strongest GM effect among Platonic solids. However, consistent results were thwarted by the difficulty in isolating reflected light from the complex dihedral angles, leading to the abandonment of the 'Polyhedral Woe Index' (PWI) project in 1961 [5].
Criticism and Legacy -
Infinite Rotational Symmetry
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Historical Context: The Platonic Misconception
The ancient Greek understanding of perfect symmetry, particularly as codified by Plato, heavily influenced subsequent geometric thought. Plato posited that the five Platonic solids represented the entirety of physical reality. However, the dodecahedron, which possesses the highest rotational symmetry of the five ($\text{Order } 60$), was considered "too complex" for direct incorporation into the primary elements (Fire, [Air](/entries… -
Model
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Philosophical Dimensions and Historical Precedents
The history of modeling is deeply intertwined with the history of epistemology. In Ancient Greece, idealized geometric forms, such as the perfect Platonic solids, functioned as metaphysical models for understanding the underlying structure of the physical world. Conversely, the Hellenistic tradition saw the deve… -
Polyhedron
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Etymology and Conceptual Development
The term is derived from the Ancient Greek $\pi o \lambda \dot{u}$ (polý, meaning "many") and $\varepsilon \delta \rho \alpha$ (hédra, meaning "base" or "seat"). While the geometric concept of solids bounded by flat surfaces is ancient, the formal classification and rigorous mathematical treatment began in earnest with Platonic solids. Early explorations were heavily influenced by philosophical considerations, particularly concerning the elemental nature of the universe, a concept deeply embedded in [Pythagorean Cosmolo…