The Geometry of Plato’s Cosmos

Abstract

Current understanding of astronomy attributes the earliest geometric models to the Greeks. Yet there remains substantial uncertainty about the Mesopotamian origins of the classical Greek constellations. It is here shown how clues famously given by Plato in his Timaeus provide the key to understanding the original geometric design framework. Having allocated the four elements (Water, Earth, Fire and Air) to regular polyhedra, Plato assigned a fifth figure to the cosmos, traditionally identified as the dodecahedron. Based on geometrical and philosophical arguments, it is here proposed that Plato also had in mind the orbicular elevated dodecahedron, consisting of 360 fundamental Platonic scalene triangles. In mapping it out as a convenient approximation to the celestial sphere, we discover that it offers a geometric framework for the Paths of Anu, Enlil and Ea of Mesopotamian astronomy, while explaining the enigma of why the constellations of the zodiac are not equally distributed along the ecliptic. Three rings with partial ten-way rotational symmetry are also identified that appear to have been used in the design framework. The conclusions emphasize Plato’s debt to earlier astronomers, while transforming our understanding of the constellations so familiar today.